What is PM equal to?
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.
- A. 10 cm
- B. 12 cm
- C. \frac{40}{3} cm ✓
- D. \frac{50}{3} cm
Correct Answer: C. \frac{40}{3} cm
Explanation
Since PM is a tangent to the circle, \angle OMP = 90^\circ. The altitude MQ from the right angle M onto the hypotenuse OP means \triangle OMQ \sim \triangle OMP. Therefore, \frac{PM}{OM} = \frac{MQ}{OQ} \implies \frac{PM}{10} = \frac{8}{6} \implies PM = \frac{80}{6} = \frac{40}{3} cm.
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