Multiple choice

Two chords AB and CD of a circle with centre O intersect each other at the point P. If ∠AOD = 20o and ∠BOC = 30o. Then ∠BPC is equal to- O केन्द्र वाले वृत्त की दो जीवायें AB तथा CD एक दूसरे को बिन्दू P पर प्रतिच्छेदित करती है। यदि ∠AOD = 20o और ∠BOC = 30o तब ∠BPC बराबर है-

  1. 50o

  2. 20o

  3. 25o

  4. 30o

Reveal answer Fill a bubble to check yourself
C Correct answer
Explanation

For intersecting chords, ∠BPC = (1/2)(arc BC + arc AD). Central angle ∠AOD = 20° subtends arc AD, so arc AD = 20°. Central angle ∠BOC = 30° subtends arc BC, so arc BC = 30°. Therefore ∠BPC = (1/2)(20° + 30°) = 25°.