Question

Circle Q has radius QR of length 55 cm. Point P is 73 cm. from Q, and PR is a tangent segment. How long is PR?

a. 18 cm.
b. 48 cm.
c. 64 cm.
d. 128 cm.

Answer 1

A tangent line is perpendicular to the radius to the point of tangency. Hence QR ⊥ PR. The Pythagorean theorem tells you
(QR)² + (PR)² = (PQ)²
(55 cm)² + (PR)² = (73 cm)²
(PR)² = 2304 cm²
(PR) = √(2304 cm²) = 48 cm

The length of PR is
b. 48 cm