Question

Prove that OP=2AP If AP and BP are two tangents and angle APB=120 degree.

Answer 1

Answer:

Step-by-step explanation:

Given: O is the centre of the circle. PA and PB are tangents drawn to a circle and ∠APB = 120°.

To prove: OP = 2AP

Proof:

In ΔOAP and ΔOBP,

OP = OP    (Common)

∠OAP = ∠OBP  (90°)    (Radius is perpendicular to the tangent at the point of contact)

OA = OB  (Radius of the circle)

∴ ΔOAP ≅ ΔOBP  (RHS congruence criterion)

⇒ ∠OAP = ∠OBP = 120°/2 = 60°

In ΔOAP,

cos ∠OPA = 60° = AP/OP

∴ 1/2 = AP/OP

⇒ OP = 2 AP

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Answer 2

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