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A, B, P are three points on a circle having centre O. If ∠OAP = 25° and ∠OBP = 35°, then the measure of ∠AOB is   (SSC CGL 1st Sit. 2013)
  • a)
    120°
  • b)
    60°
  • c)
    75°
  • d)
    150°
Correct answer is option 'A'. Can you explain this answer?
Most Upvoted Answer
A, B, P are three points on a circle having centre O. If ∠OAP = 25...
In ΔOBP.
OB = OP (radius)

∴ ∠OBP = ∠OPB = 35º
In ΔAOP
OA = OP (radius)
∴  ∠OAP = ∠OPA = 25º
Now, ∠APB = ∠OPA + ∠OPB = 25º + 35º = 60º
Hence, ∠AOB = 2∠APB
(Since, Angle be substended by arc at centre is twice the angle subtend at the perimeter)
= 2 × 60º = 120º
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Community Answer
A, B, P are three points on a circle having centre O. If ∠OAP = 25...
In ΔOBP.
OB = OP (radius)

∴ ∠OBP = ∠OPB = 35º
In ΔAOP
OA = OP (radius)
∴  ∠OAP = ∠OPA = 25º
Now, ∠APB = ∠OPA + ∠OPB = 25º + 35º = 60º
Hence, ∠AOB = 2∠APB
(Since, Angle be substended by arc at centre is twice the angle subtend at the perimeter)
= 2 × 60º = 120º
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A, B, P are three points on a circle having centre O. If ∠OAP = 25° and ∠OBP = 35°, then the measure of ∠AOB is (SSC CGL 1st Sit. 2013)a)120°b)60°c)75°d)150°Correct answer is option 'A'. Can you explain this answer?
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