The circumcenter is the center of the. circle

Answers

Answer 1

The circumcenter is the center of the circle which goes through the triangle's vertices, so the circumcenter of the triangle and the center of that circumscribed circle MUST be the same point.

The same goes for the incenter and the center of the inscribed circle, though these will not, in general, be the same point as the circumcenter.

Answer 2

Answer: Another name of circumcenter is, " Circumscribed circle ". The circumcenter is the center point of the circumcircle drawn around a polygon. The circumcircle of a polygon is the circle that passes through all of the polygon's vertices & the center of that circle is called the circumcenter. All polygons that have circumcircles are known as cyclic polygons. However, all polygons does not have a circumcircle. Only regular polygons, triangles, rectangles, and right-kites can have the circumcircle and thus the circumcenter as well.

You may find that the circumcenter of a triangle as the most common thing asked in exams and it is generally what schools begin with. So, some brief information about the circumcenter of a triangle is given below. You may safely ignore them if you haven't learned them yet.

What is the Circumcenter of a Triangle?

The circumcenter of triangle can be found out as the intersection of the perpendicular bisectors (the lines that are at right angles to the midpoint of each side) of all sides of the triangle. This means that the perpendicular bisectors of the triangle are concurrent (meeting at one point). All triangles are cyclic and hence, can circumscribe a circle, therefore, every triangle has a circumcenter.

Properties of Circumcenter of Triangle

Property 1: All the vertices of the triangle are equidistant from the circumcenter.

Property 2: All the new triangles formed by joining O to the vertices are Isosceles triangles.

Property 3: Circumcenter lies at the midpoint of the hypotenuse side of a right-angled triangle

Property 4: In an acute-angled triangle, circumcenter lies inside the triangle

Property 5: In an obtuse-angled triangle, it lies outside of the triangle

Note- Location for the circumcenter is different for different types of triangles.

How to construct Circumcenter of a Triangle?

The circumcenter of any triangle can be constructed by drawing the perpendicular bisector of any of the two sides of that triangle. The steps to construct the circumcenter are:

Step 1: Draw the perpendicular bisector of any two sides of the given triangle.Step 2: Using a ruler, extend the perpendicular bisectors until they intersect each other.Step 3: Mark the intersecting point as P which will be the circumcenter of the triangle. It should be noted that, even the bisector of the third side will also intersect at P.
Circumcenter Formula

P(X, Y) = [(x1 sin 2A + x2 sin 2B + x3 sin 2C)/ (sin 2A + sin 2B + sin 2C), (y1 sin 2A + y2 sin 2B + y3 sin 2C)/ (sin 2A + sin 2B + sin 2C)]

 ∩_∩
(„• ֊ •„)♡
┏━∪∪━━━━┓
  hope it helped
┗━━━━━━━┛

The Circumcenter Is The Center Of The. Circle
The Circumcenter Is The Center Of The. Circle

Related Questions

Determine which sequences of transformations could be applied to the parent function f(x) = x to obtain the graph of g.

Answers

Answer:

Reflect over the y-axis, vertically stretch by a factor of 3, and then shift down 1 unit

Step-by-step explanation:

Parent function:  [tex]f(x)=x[/tex]

The graph of the parent function is a straight line graph that intersects the axes at the origin (0, 0) and has a positive slope of 1 unit.

To determine the sequence of transformations, find the equation of the transformed function in slope--intercept form.

Slope-intercept form of a linear function:  [tex]f(x)=mx+b[/tex]

(where m is the slope and b is the y-intercept)

To calculate the slope of the transformed function, choose two points on the line and use the slope formula:

Let (x₁, y₁) = (0, -1)Let (x₂, y₂) = (1, -4)

[tex]\implies \sf slope\:(m)=\dfrac{y_2-y_1}{x_2-x_1}=\dfrac{-4-(-1)}{1-0}=-3[/tex]

The y-intercept (where the line crosses the y-axis) of the transformed function is (0, -1).

Therefore the equation of the transformed function is:

[tex]g(x)=-3x-1[/tex]

Translations

For a > 0

[tex]f(x+a) \implies f(x) \: \textsf{translated}\:a\:\textsf{units left}[/tex]

[tex]f(x-a) \implies f(x) \: \textsf{translated}\:a\:\textsf{units right}[/tex]

[tex]f(x)+a \implies f(x) \: \textsf{translated}\:a\:\textsf{units up}[/tex]

[tex]f(x)-a \implies f(x) \: \textsf{translated}\:a\:\textsf{units down}[/tex]

[tex]y=a\:f(x) \implies f(x) \: \textsf{stretched parallel to the y-axis (vertically) by a factor of}\:a[/tex]

[tex]y=f(ax) \implies f(x) \: \textsf{stretched parallel to the x-axis (horizontally) by a factor of} \: \dfrac{1}{a}[/tex]

[tex]y=-f(x) \implies f(x) \: \textsf{reflected in the} \: x \textsf{-axis}[/tex]

[tex]y=f(-x) \implies f(x) \: \textsf{reflected in the} \: y \textsf{-axis}[/tex]

Comparing the transformed function's equation with the parent function:

[tex]\begin{cases}f(x)=x\\g(x)=-3x-1\end{cases}[/tex]

Transformations

1.  Reflection in the y-axis:

    [tex]f(-x)=-x[/tex]

2.  Vertically stretched by a factor of 3:

    [tex]3f(-x)=-3x[/tex]

3.  Shifted 1 unit down:

    [tex]3f(-x)-1=-3x-1[/tex]

Summary

Reflect over the y-axis, vertically stretch by a factor of 3, and then shift down 1 unit

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What is the 25th term of this arithmetic sequence? 3,9,15,21,27

Answers

Answer:

75

Step-by-step explanation:

you need to divide numbers by 3

3×25=75

Answer:

147

Step-by-step explanation:

Arithmetic sequence:

  a = first term = 3

  d = common difference = second term - first term

     = 9 - 3

  d = 6

  n = 25

  [tex]\sf \boxed{\bf n^{th} \ term = a + (n-1) d}[/tex]

                   = 3 + (25 - 1)*6

                   = 3 + 24*6

                    = 3 + 144

                    = 147

if AB= 51, and AC = 120. find BC.
A
B
C

Answers

Answer:

Step-by-step explanation:

AB = 51

AC = 120

BC = AC - AB

BC = 120-51

BC = 69 units

How do I prove this so that angle 3 and angle 4 are complimentary?

Answers

Answer:

please see analysis

Step-by-step explanation:

Reason

1.) given

2.) definition of amptimentaly angle LS

3.) substitution property

4.)definition of amptimentaly angle

hope it helps thank me later

An isosceles triangle has two sides of equal length, a, and a base, b. The perimeter of the triangle is 15.7 inches, so the equation to solve is 2a + b = 15.7.

Shana wants to use all 62 feet of the fencing she has to make a rectangular run for her dog. She decides to make the length of the run 20 feet. She writes and solves the equation 2 l plus 2 w equals 62 to find the width of the run.

Which statements are true of the solution? Check all that apply.

The value of w is 10 feet.
The value of w can be zero.
The value of w cannot be a negative number.
Substitution is used to replace the variable l with a value of 20.
The subtraction property of equality is used to isolate the term with the variable w.

Answers

Answer:

  [c] The value of w cannot be a negative number.

  [d] Substitution is used to replace the variable l with a value of 20.

  [e] The subtraction property of equality is used to isolate the term with the variable w.

Step-by-step explanation:

     To figure out which steps of the solution are true, let us solve.

2 l plus 2 w equals 62 -> 2l + 2w = 62

----

2l + 2w = 62

2(20) + 2w = 62  <- Substitution is used to replace the variable l with a value of 20.

40 + 2w = 62

2w = 22 <- The subtraction property of equality is used to isolate the term with the variable w.

w = 11

     This means that the value of w is not 10 feet so the first option is incorrect. This shape is a rectangle, so the value of w cannot be 0. Since we cannot have a negative measurement, option three is incorrect. This leaves us with the last three options as our answer, shown by the work above.

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what is 1/5 plus 1/10

Answers

Step-by-step explanation:

hope it helps you and give me a brainliest

Step-by-step explanation:

[tex] = \frac{1}{5} + \frac{1}{10} \\ [/tex]

Now make the denominator same...

[tex] = \frac{1}{5} \times \frac{2}{2} + \frac{1}{10} \\ [/tex]

[tex] = \frac{2}{10} + \frac{1}{10} \\ [/tex]

[tex] = \frac{3}{10} \\ [/tex]

:)

..

Select the correct answer.
Which equation is true for the value b = 2?
A.
2b + 24 = 30
B.
3b − 2 = 4
C.
b + 4 = 8
D.
2b − 3 = 0

Answers

The answer is (B) 3b-2=4

Write the sentence as an equation.

253 equals the product of 232 and k


Type a slash ( / ) if you want to use a division sign.

Answers

Answer:

253=232×k

Step-by-step explanation:

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When a number is divided into by 8,9,and 6 the remainders are 7, 8 and 5 respectively. Find the number

Answers

Answer:71

Step-by-step explanation:

71 is the number when it is divided into by 8,9,and 6 the remainders are 7, 8 and 5

What is Number system?

A number system is defined as a system of writing to express numbers.

Given that a number is divided into by 8,9,and 6 the remainders are 7, 8 and 5 respectively.

We need to find the number.

In division there are three parts the divider, dividend, quotient, and remainder.

Let us find the LCM of 8,9 and 6

LCM of 8, 9,6 is 72

72-1=71

Hence, 71 is the number when it is divided into by 8,9,and 6 the remainders are 7, 8 and 5

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ها ( در محمود) و
Which expression is equivalent to
O
x²7 (3√7)

Answers

Step-by-step explanation:

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How do you write an equation in function form?

Answers

Answer: Writing an equation in function form. You want to remove the x term from the side y is on and move it to the other side of the equal sign. To do this either add or subtract the x term from both sides. Next divide by the coefficient of the y term. Now your equation is in function form.

explanation: like 57 * Y =142500

what is the number for Y if u don't know u could divided 142500 by 57 and it equals? 2500;) hope I helped

Mr. avanzado has an underground in his house. what unit of measure will he use to find its value

Answers

Answer:  Volume

Step-by-step explanation:

5.
Annette earns $30 in 2 hours and Carla earns $96 in 6 hours. Who has the
higher hourly rate?
A

Answers

Answer is Carla at $16/hr
Reason
Annette makes $30/2 hrs
Divide and it makes $15/1 hrs
Carla makes $96/6 hrs
Divide and it makes $16/hr

Answer:

Carla

Step-by-step explanation:

First we need to find the hourly rate for Annette

Take the dollars earned and divide by the number of hours

30/2 = 15 dollars per hour

Now we can find the hourly rate for Carla

96/6 =16 dollars per hour

Carla has the higher hourly rate  since she earns more per hour

The figure shows part of the concrete slab which is used to make drains and its cross-section. it is made up of a cuboid of dimensions 120 cm by 60 cm by 40 cm, with a half-cylinder horizontally carved out of it.

(i) find the area of the cross-section ABCDEFG.
(ii) find the volume of the concrete slab.
(iii) find the total surface area of the concrete slab.
(iv) find the mass of the concrete slab if the density of concrete is 2300 kg/cubic m, giving your answer in kg.

Answers

(i) The area of the cross section ABCDEFG is 1771.6cm³

(ii) The volume of the concrete lab is 212592 cm³

(iii) the total surface area of the concrete slab is 30284 cm²

(iv) The mass of the concrete slab is 40746.8 kg/m³.

Given, dimensions are 120 cm by 60 cm by

40 cm.

(i) area of cross section = 40 × 60 ₋ π(60 ₋10 ₋ 10)/2 . 1/2

                                     = 1771.6 cm³

(ii) the volume of the concrete slab = 40 × 60 × 120 ₋ 1/2 π((60 ₋ 10   ₋10)/2)² . 120

= 212592 cm³

(iii) The total surface area is:

=40 × 120 × 2 ₊ 60 × 120 ₊ 1771.6 × 2 ₊ 10 × 120 × 2 ₊ 1/2 π(60 ₋ 10 ₋10) × 120

= 30284 cm²

(iv) Mass of the concrete slab given density is 2300 kg/m³

Mass = Volume × density

Mass = 17.716 m³ ×  2300

         = 40746.8 kg/m³

Hence we get the mass as 40746.8 kg/m³.

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The graphs below have the same shape. The equation of the blue graph is f(x)
=|x|. Which of these is the equation of the red graph, g(x)?
y f(x) = |x|
A. g(x)=|x-5|
B. g(x)=|xl-5
C. g(x)=|x + 5|
D. g(x)=|x|+5

Answers

The required correct answer is C. g(x) = |x + 5|. This equation satisfies both conditions we identified above: it involves the term "x+5", and it shifts the graph of f(x) = |x| to the left by 5 units.

What are functions?

Functions is the relationship between sets of values. e g y=f(x), for every value of x there is its exists in a set of y. x is the independent variable while Y is the dependent variable.

Here,
Since both graphs have the same shape, the red graph is a transformation of the blue graph.

When we compare the two graphs, we can see that the red graph is shifted horizontally to the left by 5 units. This means that the equation of the red graph must involve the term "x+5" or "x-5" in some way.

Also, we can see that the red graph intersects the y-axis at the point (0, 5). This means that the equation of the red graph must involve the term "+5" in some way.

The correct answer is C. g(x) = |x + 5|. This equation satisfies both conditions we identified above: it involves the term "x+5", and it shifts the graph of f(x) = |x| to the left by 5 units. When we plot this equation, we get a graph that has the same shape as f(x) = |x|, but is shifted to the left and intersects the y-axis at (0, 5).

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which expression is equivalent to. 5 32x^5 y ^10 z^15

HURRY NOW

Answers

Answer:

the answer is B

Step-by-step explanation:

5th root of 32 = 2

5 / 5 = cancels

10 / 5 = 2

15 / 5 = 3

2xy²z³

Answer:

2xy^2z^3

Step-by-step explanation:

If the size of a storage box is 50 cm by 10 cm by 20 cm. What is the volume of the box?

Answers

Answer:

l×b×h

50×10×20

10000cm^3

Step-by-step explanation:

please mark me as brainlest

Answer:

10000 cm³

Step-by-step explanation:

Volume of rectangular box:

         To find the volume of box,  multiply the length, width and height of the box and its unit is cubic units

         [tex]\sf \boxed{\bf Volume \ of rectangular \ box = l *w*h}[/tex]

                                                         = 50 * 1 0 * 20

                                                          = 10000 cm³

What function is represented below?
HELP ASAP!!

Answers

f(x)= (1/4)^x -2 the negative two is not with the x

Answer:

C

Step-by-step explanation:

(1/4)^x-2 is the answer

A farmer has 32 cows. he puts an equal number of cows in 4 fields. each cow produces 6 gallons of milk. how much milk do the cows in one field produce?

Answers

Answer:

48/field

you take 32÷4=8 and then you 8*6=48 each field

I'm having problems because our teacher is making us do this monstersety 391.92x10372.45-918+12.5

Answers

Answer:

4064265.104

Step-by-step explanation:

Use PEMDAS :

Parentheses, Exponents, Multiplication, Division, Addition, Subtraction.

We only have multiplication and addition/subtraction to do. Multiplication and Division can go in either order depending on which comes first reading left to right. It's the same with Addition and Subtraction: we will first subtract 918 and then add 12.5.

Let's start by Multiplying. 391.92 x 10372.45 = 4065170.604.

Now, subract 918. 4065170.604-918 = 4064252.604.

Finally, add back 12.5. 4064252.604. +12.5 = 4064265.104 !

find the magnitude of each of the following vectors 4i-8j​

Answers

Answer:

magnitude of a shown vector is

[tex]4 \sqrt{5} [/tex]

PLEASE ANSWER ASAP!!!!!11
The nth term of a sequence is represented by 2n^3+25n^2+32n−15/ 6n^4+2n^3−11n^2−2n+17.

What is the limit of the the nth term as x becomes increasingly large?

A. 0
B. 1/3
C. 3
D. The limit does not exist

Answers

The limit of the nth term of a sequence does not exist option (D) is correct.

What is the limit?

A limit is a value at which a function approaches the output for the given values in mathematics. Limits are used to determine integrals, derivatives, and continuity in calculus and mathematics.

We have an expression:

[tex]= \rm \dfrac{2n^5+25n^2+32n-15}{6n^4+2n^3-11n^2-2n+17}[/tex]

Applying limit:

[tex]= \lim_{n \to \infty} \rm \dfrac{2n^5+25n^2+32n-15}{6n^4+2n^3-11n^2-2n+17}[/tex]

[tex]=\lim _{n\to \infty \:} n \left(\dfrac{2+\dfrac{25}{n^3}+\dfrac{32}{n^4}-\dfrac{15}{n^5}}{6+\dfrac{2}{n}-\dfrac{11}{n^2}-\dfrac{2}{n^3}+\dfrac{17}{n^4}}\right)[/tex]

= ∞ = The limit does not exist

Thus, the limit of the nth term of a sequence does not exist option (D) is correct.

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Question 4) Identify the surface area of the composite figure.

4 4 in. FRIZERSLI 15 in. 4 in. 4 in. THE # # ill 7 in. 10 in. Question 4 ) Identify the surface area of the composite figure . 4 4 in . FRIZERSLI 15 in . 4 in . 4 in . THE # # ill 7 in . 10 in . ​

Answers

The surface area of the composite figure is given by 730 sq.in

What are Composites ?

Composites are solid figures made up of basic shapes like rectangle , square and even of three dimensional figures like cube , cuboid etc.

It is given in the question to determine the area of the composite figure

Area of Cube is

Area = 6 * side²

Area = 6 * 4² = 96 sq.in

The surface area of the cuboid is equal to

Sum of surface area of all the sides

As the opposite sides are same

7x10x2 + 15x10x2 + 7x15x2

650 sq.in

As the surface area of the base of the cube is counted twice

Therefore it will subtracted from the total

96 + 650 - 4*4

=730 sq.in

Therefore the surface area of the composite figure is given by 730 sq.in

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A music-streaming service charges $9 per month for a single user. Additional users within the same household can be added for $3 per month.
Write an equation that shows how the monthly cost, y, depends on the number of additional users in the household, x.
Do not include dollar signs in the equation.
y=

Answers

Answer:

y=9+3x

Step-by-step explanation:

It starts with y=.

Then you have to put the 9 for the streaming service.

Then you add.

You multiply by 3 for all the x in the household plan.

Answer:

y = 9 + 3x

Step-by-step explanation:

$9 per month for a single user

$3 per month for additional users

Find monthly cost, y, where additional cost is represented by x

The cost for a single user = fixed cost (It remains constant)

The cost of the additional user = variable (It increases with the number of users)

The monthly cost increases with the number of additional users

The monthly cost = cost of single user + the cost of additional users

y = 9 + 3x

What is the rate of change of the amount earned with respect to hours worked for this function?

Answers

Answer:

72

Step-by-step explanation:

I got to get some bread for you guys

Answer:

I'll do it the answer is truthfully 72 if you don't think go check my page

Question
Ahmet borrows $700 and is charged compound interest at 15% per year. How much will he have to pay back in total after 6
years?
Give your answer to two decimal places.

Answers

Answer:

I did 700 - 15% times that answer by 6 and u get that big answer.

The required amount Ahmet needs to pay after 6 years is $1619.14.

What is compound interest?

Compound interest is the interest on deposits computed on both the initial principal and the interest earned over time.

Amount = principal[1 + r/n]ⁿᵃ

Principal = P rate= r Time =a  , n = compounding frequency

Here,

From the given data,
P = 700, r = 15% and t = 6 (n =1)

Now,
Amount = principal[1 + r/n]ⁿᵃ
Amount = 700(1 + 0.15)⁶
Amount = $1619.14

Thus, the required amount Ahmet needs to pay after 6 years is $1619.14.

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2. Draw a picture to show how many 1/5s there are in 7/10.​

Answers

2. 7/10 ÷ 1/5 = 7/2

7/10 × 5 = 1/2

hope it helps u

i need this for sparx hwk

Answers

Only b and c but i hope that i helped

What is the slope of the line represented by the equation y = -x + 1/2x+1/4

- 1/2

- 1/4

1/4

1/2

Answers

I don’t know it to bad………

1. In the following diagram, PQRS is a square of side 8 cm. PQ, QR, RS and SP are semi-circular arcs with centres at the midpoint of the sides of the square. Find the area of theshaded region.

Answers

Answer:

Step-by-step explanation:

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