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2 years ago

Given: Circle X with a Radius r and circle Y with radius s Prove: Circle x is similar to circle y

Mathematics

2 answers:

lana [24]2 years ago

8 0

Two figures are similar if one is the scaled version of the other.

This is always the case for circles, because their geometry is fixed, and you can't modify it in anyway, otherwise it wouldn't be a circle anymore.

To be more precise, you only need two steps to prove that every two circles are similar:

Translate one of the two circles so that they have the same center
Scale the inner circle (for example) unit it has the same radius of the outer one. You can obviously shrink the outer one as well

Now the two circles have the same center and the same radius, and thus they are the same. We just proved that any two circles can be reduced to be the same circle using only translations and scaling, which generate similar shapes.

Recapping, we have:

Start with circle X and radius r
Translate it so that it has the same center as circle Y. This new circle, say X', is similar to the first one, because you only translated it.
Scale the radius of circle X' until it becomes $s$ . This new circle, say X'', is similar to X' because you only scaled it

So, we passed from X to X' to X'', and they are all similar to each other, and in the end we have X''=Y, which ends the proof.

stealth61 [152]2 years ago

5 0

Answer:

Step-by-step explanation:

You might be interested in

Match each pair of points to the equation of the line that is parallel to the line passing through the points.

Paraphin [41]

we know that

If two lines are parallel, then, their slopes are equal.

The formula to calculate the slope between two points is equal to

$m=\frac{y2-y1}{x2-x1}$

we will proceed to calculate the slope in each case, to determine the solution of the problem

Case A) Point $B(5,2)\ C(7,-5)$

Find the slope BC

Substitute the values in the formula

$m=\frac{-5-2}{7-5}$

$m=\frac{-7}{2}$

$m=-3.5$

The equation $y=-3.5x-15$ is parallel to the line passing through the points $B(5,2)\ C(7,-5)$

therefore

the answer Part A) is

$B(5,2)\ C(7,-5)$ ------> $y=-3.5x-15$

Case B) Point $D(11,6)\ E(5,9)$

Find the slope DE

Substitute the values in the formula

$m=\frac{9-6}{5-11}$

$m=\frac{3}{-6}$

$m=-0.5$

The equation $y=-0.5x-3$ is parallel to the line passing through the points $D(11,6)\ E(5,9)$

therefore

the answer Part B) is

$D(11,6)\ E(5,9)$ ------> $y=-0.5x-3$

Case C) Point $F(-7,12)\ G(3,-8)$

Find the slope FG

Substitute the values in the formula

$m=\frac{-8-12}{3+7}$

$m=\frac{-20}{10}$

$m=-2$

Any linear equation with slope $m=-2$ will be parallel to the line passing through the points $F(-7,12)\ G(3,-8)$

Case D) Point $H(4,4)\ I(8,9)$

Find the slope HI

Substitute the values in the formula

$m=\frac{9-4}{8-4}$

$m=\frac{5}{4}$

$m=1.25$

The equation $y=1.25x+4$ is parallel to the line passing through the points $H(4,4)\ I(8,9)$

therefore

the answer Part D) is

$H(4,4)\ I(8,9)$ ------> $y=1.25x+4$

Case E) Point $J(7,2)\ K(-9,8)$

Find the slope JK

Substitute the values in the formula

$m=\frac{8-2}{-9-7}$

$m=\frac{6}{-16}$

$m=-0.375$

Any linear equation with slope $m=-0.375$ will be parallel to the line passing through the points $J(7,2)\ K(-9,8)$

Case F) Point $L(5,-7)\ M(4,-12)$

Find the slope LM

Substitute the values in the formula

$m=\frac{-12+7}{4-5}$

$m=\frac{-5}{-1}$

$m=5$

The equation $y=5x+19$ is parallel to the line passing through the points $L(5,-7)\ M(4,-12)$

therefore

the answer Part F) is

$L(5,-7)\ M(4,-12)$ ------> $y=5x+19$

8 0

1 year ago

Read 2 more answers

GRAHAM CORPORATION

astra-53 [7]

Answer:

<h2>Net proceed= s-0.98nd-11</h2>

Step-by-step explanation:

Given that the shares cost $d

n shares will be =$dn

paid 2% commission to her broker= (2/100)*nd= 0.02nd

sold the share for $s

paid a fee of $11

Her net proceeds algebraically will be

Net proceed= s-nd-11-0.02nd

collect like terms

Net proceed= s-(nd-0.02nd)-11

Net proceed= s-0.98nd-11

5 0

1 year ago

A 20-person fraternity is making their weekend plans around 5 different parties in IV. Each brother will attend exactly one of t

skad [1K]

Answer:

3876

Step-by-step explanation:

Given the following :

Fraternity members = 20

They are to attend 5 different parties in groups of 4

Meaning a group = 4 persons

Atleast one brother will attend exactly one of the parties. (the brothers are indistinguishable).

Then, exactly one brother at a party (20 - 1) = 19, since they are indistinguishable.

Group members are in 4's

19C4

From: nCr = n! /(n-r)! r!

19C4 = 19! / (19 - 4)! 4!

= 19! / 15! 4!

= (19 * 18 * 17 * 16) / (4 * 3 * 2)

= 93024 / 24

= 3876

3 0

2 years ago

In a scale drawing of an apartment 1 centimeter represents 2 3/4 feet. if the length of the kitchens is 4 1/2 cm on the scale dr

rusak2 [61]

Given: 1 cm = 2 3/4 ft ; kitchen length = 4 1/2 cm
2 3/4 = 11/4; 4 1/2= 9/2

11/4 x 9/2 = 99/8 =12 3/8

OR You could use decimals

2 3/4 = 2.75 ; 4 1/2 = 4.5
2.75 x 4.5 = 12.375
12.375 = 12 375/1000 or 12 3/8

5 0

2 years ago

The figure shown is often used to prove the Pythagorean theorem. Part of the proof is

mixas84 [53]

Answer:

if you need hlep with any thing we can do a zoom if you now how to set it up.

Step-by-step explanation:

7 0

2 years ago