A tangent AP, P-point of tangency is drawn to a circle with center O. Find the radius of the circle if OA = 15, AP = 12.

The radius OP drawn to the tangent point is perpendicular to the tangent AP. In a right-angled triangle AOP, the radius of the OP is the leg. From the Pythagorean theorem OP ^ 2 = AO ^ 2 – AP ^ 2.
RR ^ 2 = 15 ^ 2 – 12 ^ 2 = 225 – 144 = 81;
OR = √81 = 9.
Answer: the radius of the circle = 9.




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