Multiple choice

In a circle O is centre diameter PQ cut chord MN at O'. If ∠NOQ=108o and QM=QN then find the value of ∠PO'N. एक वृत्त में O केन्द्र है जीवा MN और व्यास PQ एक दूसरे को O' पर काटते हैं। यदि ∠NOQ=108o और QM=QN है तो ∠PO'N का मान ज्ञात कीजिए।

  1. 72o

  2. 108o

  3. 90o

  4. 36o
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C Correct answer
Explanation

Given ∠NOQ = 108° and QM = QN, triangle NQM is isosceles at Q. In circle geometry, when a diameter (PQ) intersects a chord (MN) at O', if QM = QN, then O' is the midpoint of MN. Since PQ is a diameter passing through center O, and O' lies on MN, the line PO'N is perpendicular to MN. Therefore ∠PO'N = 90°.

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