Question

चित्र में, वृत्त का केंद्र O है। यदि angle AOB = 900 तथा angle PBA = 300 हो तो angle PA की माप ज्ञात कीजिए।

Answer 1

∠PAB = 105° , ∠PAO  = 60°

Step-by-step explanation:

∠AOB = 90°

∠AOB = 2∠APB   ( angle by same chord at center & arc)

=> 90° = 2∠APB

=> ∠APB  = 45°

 

∠APB + ∠PAB + ∠PBA = 180°

=> 45°  + ∠PAB + 30° = 180°

=> ∠PAB = 105°

ΔOAB

OA = OB  ( radius)

=> ∠OAB = ∠OBA

∠OAB +  ∠OBA + ∠AOB = 180°

=> 2∠OAB  + 90° = 180°

=> ∠OAB = 45°

∠PAB = ∠PAO + ∠OAB

=> 105° = ∠PAO + 45°

=> ∠PAO  = 60°

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