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If tangents PA and PB from a point P to a circle with centre O are inclined to each other at angle of 80

o

, then ∠POA is equal to.

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Correct option is A)

Given: ∠APB=80

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As we know that sum of ∠APB+∠AOB=180

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(Using Property)

∠AOB=100

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Δ AOP ≃ ΔBOP by SSS congruency criteria.

AO=BO (Radius of circle)

PO=PO (common side of triangle)

AP=BP (tangents form an external point)

∠AOP=∠BOP (CPCT )

∠POA+∠POB=∠AOB=100

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∠POA=50

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