Question

Circle P is congruent to Circle Q
Segment AB is congruent to Segment CD
Segment AB = 24
Segment PX = 9
Using the Pythagorean Theorem, find the length of the radius of Circle Q

Pic included in comments

Answer 1

I used the Pythagorean theorem and came up with
x=25.6

Answer 2

24 divides in half to be the side of one triangle. So the length of CY is 12. You can use the Pythagorean theorem with those values and you'll get the radius.

Answer 3

12^2+9^2=c^2
would this be the right equation?

Answer 4

Yes.

Answer 5

c=15?

Answer 6

Yes. That's correct.

Answer 7

Thank you very much. Now do you always divide the first segment by two (AB) when you first start the equation?

Answer 8

For example, say I have this problem right here:

Circle R is congruent to Circle S
The radius of Circle S is 25
Segment SY and is congruent to Segment RX
Segment SY = 15
Using the Pythagorean Theorem find the length of Segment AB


Would I divide segment SY by two and then use the answer in the Pythagorean theorem?

Answer 9

In this, you have to find the length of YD, which is half of CD. Once you find YD, you can double that so that it equals the length of CD. Because the circles are congruent, CD=AB. So when you find the length of CD, you found the length of AB.

Answer 10

The hypotenuse is the radius. So, you use 15^2+b^2=25^2 and solve for b.

Answer 11

b=20

Answer 12

Yes. That's only YD. CD is double that.

Answer 13

so it is 40

Answer 14

Correct. CD=40. The circles are congruent so CD=AB. Therefore, AB=40

Answer 15

ok, thank you :)

Answer 16

You're welcome. Glad to help :)