From a point P, a tangent is drawn to a circle with center O. The radius is 9 cm, and the distance from O to P is 15 cm. What is the length of the tangent?
Show answer & explanation
Correct answer: B
Explanation
Given:
Radius of the circle (OT) = 9 cm
Distance from the center to the external point (OP) = 15 cm
Length of the tangent = PT
Since the radius is perpendicular to the tangent at the point of contact, △OPT is a right-angled triangle.
By the Pythagorean theorem,
PT² = OP² − OT²
= 15² − 9²
= 225 − 81
= 144
PT = √144= 12 cm