Multiple choice

Two chords PQ and RS of a circle with centre O intersect each other at A. If ∠POR = 100o and ∠SPA = 30o then what is the measure of ∠PAR if PR and QS intersect each other on extending at E. O केन्द्र वाले वृत्त में दो जीवायें PQ और RS एक दूसरे को A पर काटती हैं। यदि ∠POR 100o और ∠SPA = 30o तो ∠PAR की माप क्या है? यदि PR और QS एक दूसरे को बढ़ाने पर बिन्दु E पर काटते हैं।

  1. 77o

  2. 80o

  3. 85o

  4. 90o
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B Correct answer
Explanation

Using the intersecting chords theorem, the angle between two chords equals half the sum of the arcs they intercept. Given ∠POR = 100° is the central angle subtended by arc PR, and ∠SPA = 30° at the intersection point A, we can determine that ∠PAR = 80° by applying the vertical angles property and angle sum relationships in the quadrilateral formed by the intersecting chords.

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