Question

CBSE CLASS X

Circles - Mathematics

Answer 1

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Answer 2

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AP is the tangent to the circle

OA _|_ AP (Radius is perpendicular to the tangent at the point of contact)

∠OAP = 90 degrees

In angle OAP, 

Sin ∠OPA= OA/OP = R/2R = 1/2

∠OPA = 30

In Angle ABP,

AP = BP

∠PAB = ∠PBA

so 60+ ∠PAB + ∠PBA = 180

60+2 ∠PAB = 180

∠PAB = 180 - 60/2

∠PAB = 60

But

as ∠OAP = OBP = 90

OAP = OBP

so,

60 + x = 90

x = 30

therefore,

∠OTS = OST= 30

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