Multiple choice

Two chords PQ and RS of circle whose center is O, Meets at point T and ∠POR = 60o,∠QOS = 50o, then the value ∠QTS is- केन्द्र "O" वाले वृत्त की दो जीवाएँ PQ एंव RS एक दूसरे को T पर मिलती है , एवं ∠POR = 60o,∠QOS = 50o तो ∠QTS का मान है -

  1. 55o

  2. 45o

  3. 75o

  4. 90o
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A Correct answer
Explanation

For intersecting chords in a circle, the angle formed at the intersection point equals half the sum of the measures of the arcs intercepted by the angle and its vertical angle. Here, ∠QTS = 1/2(arc(QS) + arc(PR)). Given ∠QOS = 50° and ∠POR = 60°, the sum of these central angles is 110°, and ∠QTS = 110°/2 = 55°.

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