Question

Line segment KL is tangent to circle J at point K.



What is the length of the radius, r?

8 units
10 units
12 units
16 units

Answer 1

JK and KL are the legs that are r and 24 units long respectively

JL is the hypotenuse and it is r+16 units long

we have a right triangle, so we use the pythagorean theorem to find r

a^2 + b^2 = c^2

r^2 + 24^2 = (r+16)^2

solve for r

Answer 2

Okay gimmie a moment

Answer 3

i plug the r into the calc?

Answer 4

what happens when you expand out (r+16)^2 ?

Answer 5

use FOIL or the box method

Answer 6

I got this

Answer 7

so you'll have

r^2 + 24^2 = (r+16)^2
r^2 + 576 = r^2+32r+256
576 = 32r+256 .... the r^2 terms cancel after you subtract r^2 from both sides

do you see how to finish up?

Answer 8

yes

Answer 9

okay so i got 10

Answer 10

yep, nice work, the answer is r = 10