A tangent XY at point X of a circle with radius 7 cm meets a line through the center O at point Y such that OY = 25 cm. What is the length of the tangent XY?
Show answer & explanation
Correct answer: C
Explanation
Given:
Radius (OX) = 7 cm
OY = 25 cm
The radius OX is perpendicular to the tangent XY; therefore, △OXY is a right-angled triangle.
By the Pythagorean theorem:
XY² = OY² - OX²
= 25² - 7²
= 625 - 49
= 576
XY = √576
= 24 cm