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use trigonometric ratios.
monikasree:
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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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