Answer:
The radius of the circle is 18.
Explanation:
Since you have a right triangle, you can use Pythagorean Theorem.
a^2 + b^2 = c^2
or leg^2 + leg^2 = hypotenuse^2
One leg is r and the other leg is 24. The hypotenuse is r+12.
This gives us:
r^2 + 24^2 =(r+12)^2
r^2 + 576 = r^2+24r+144
I just squared the 24 on the left side of the equation. And squared r+12 on the right side of the equation.
subtract r^2 from both sides.
576 = 24r + 144
subtract 144
432 = 24r
divide by 24
18 = r
The radius r, of the circle is 18.