2024 · Q59
Consider the following for the next three (03) items that follow: Let MN be a chord of length 16 cm of a circle with centre at O and radius 10 cm. The tangents at M and N intersect at a point P. Further, OP intersects MN perpendicularly at Q. What is PM equal to?
Elementary MathematicsGeometry: Lines, Angles and Triangles
- A10 cm
- B12 cm
- C40/3 cm
- D50/3 cm
Explanation
In right ΔOPM (∠OMP = 90° since PM is tangent), QM is the altitude to hypotenuse OP, so MQ² = OQ·QP. With MQ = 8 and OQ = 6 (Q58): 64 = 6·QP, so QP = 32/3. Then PM = √(QP² + MQ²) = √(1024/9 + 576/9) = √(1600/9) = 40/3 cm — option C.