Question

Two tangents PA and PB are drawn to the circle with centre O, such that

angle APB = 120°. Write the measure of angle OAB.​

Answer 1

Answer:

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O is the center of the given circle

∠OAP=∠OBP=90⁰

(Radius is perpendicular to the tangent at the point of contact)

OA=OB

(radius of the circle)

∴△OAP is congruent to △OBP

So that, 

∠OPA=∠OPB=120/2=60⁰

In △OAP

cos∠OPA=cos60=OPAP{cos60⁰=1/2}

1/2 =AP/ OP

OP=2AP 

Hence proved

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