What is OQ 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. 5 cm
- B. 6 cm ✓
- C. 7 cm
- D. 8 cm
Correct Answer: B. 6 cm
Explanation
A perpendicular drawn from the center to a chord bisects the chord, so MQ = \frac{16}{2} = 8 cm. In right-angled \triangle OMQ, using Pythagoras theorem, OQ = \sqrt{OM^2 - MQ^2} = \sqrt{10^2 - 8^2} = 6 cm.
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