Question

please answer my question​

Answer 1

Let OA = OC = r ... (i) (radii of same circle)

In ∆OAB, angle OAB = 90° ... (radius _|_ tangent)

OB² = OA² + AB² ... (Pythagorean Theorem)

(OC + CB)² = OA² + AB²

(r + 8)² = r² + 12²

r² + 16r + 64 = r² + 144

16r = 144 - 64

16r = 80

r = 5 cm

Hence, radius of the circle is 5 cm.