The length of a direct common tangent to two circles is 12 cm. Their centers are 13 cm apart. If the larger circle has a radius of 8 cm, what is the radius of the smaller circle?
Show answer & explanation
Correct answer: B
Explanation
For a straight bisecting tangent:
d² = l² + (R − r)²
where d = 13, l = 12, R = 8, r = smaller radius
13² = 12² + (8 − r)²
169 = 144 + (8 − r)²
(8 − r)² = 25
8 − r = 5
r = 3 cm