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In fig. tangent segments PS and PT are drawn to a circle with centre O such that< SPT120".Prove that OP= 2 PS |
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Answer» Consider ΔOPS and ΔOPTOS = OT ( radii)∠OSP = ∠OTP = 90 (tangents are perpendicular to the radii)SP = ST ( tangents to a circle from the external point are congruence)ΔOPS ≅ ΔOPT ( By SAS criterion)The corresponding parts of the corresponding triangles are congruent.∠OPS = ∠OPTsince ∠SPT = 120° and ∠OPS = ∠OPTwe have ∠OPS = ∠OPT = 60°∠POS = ∠POT = 30°Consider In a ΔPOSsin 30° = PS / OP1 / 2 = PS / OPOP = 2PS. |
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