Question

Tangent PA and tangent PB are drawn to the circle with centre O, such that angle APB = 120°. Prove that OP = 2AP. (Point P is in exterior of a Circle)

Answer 1

student-name Enrique Iglesias asked in Math
Two tangent segments PA and PB are drawn to a circle with centre O, such that angle APB= 120degree. Prove that OP=2AP.

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student-name Lalit Mehra answered this
27767 helpful votes in Math, Class XI-Science


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)

In ΔOAP,

⇒ OP = 2 AP

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