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Question


Which of the following statement(s) is/are correct with reference to the figure?
  1. PA = OB, ∠APO = ∠BPO
  2. ∠AOP = ∠BOP, ∠APO = ∠BOP
  3. PA = PB, ∠APO =∠BPO
  4. OA = OB, ∠AOP = ∠BOP


Solution

The correct options are
C PA = PB, ∠APO =∠BPO
D OA = OB, ∠AOP = ∠BOP

In the given figure, the tangents PA and PB are equal in length, because tangents from an external point are equal in length.

∠APO = ∠BPO, because tangents from an external point are equally inclined to the line joining the point and the centre of the circle i.e., OP.

OA = OB (radius of the circle).
∠AOP = ∠BOP because tangents from an external point subtend equal angle at the centre of the circle.

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