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27. In the adjoiningfigure, from anexternal point Ptwo tangents PTand PS are drawn toa circle with centreO and radius r. IfOP 2r, then showthat LOTS = <OST= 30°CBSE 2016 |
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Answer» AP is the tangent to the circleOA _|_ AP (Radius is perpendicular to the tangent at the point of contact)∠OAP = 90 degreesIn angle OAP,Sin∠OPA= OA/OP = R/2R = 1/2∠OPA = 30In Angle ABP,AP = BP∠PAB =∠PBAso 60+∠PAB +∠PBA = 18060+2∠PAB = 180∠PAB = 180 - 60/2∠PAB = 60Butas∠OAP = OBP = 90OAP = OBPso,60 + x = 90x = 30therefore,∠OTS = OST= 30 |
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