prove that tangents from an external point to a circle are equal in le

1.	prove that tangents from an external point to a circle are equal in length
Answer» Given: P is an external point to the circle C(O,r).PQ and PR are two tangents from P to the circle.To Prove: PQ = PRConstruction: Join OPProof:{tex}\\because{/tex}\xa0A tangent to a circle is perpendicular to the radius through the point of contact{tex}\\therefore{/tex}{tex}\\angle{/tex}OQP = 90o = {tex}\\angle{/tex}ORPNow in right triangles POQ and POR,OQ = OR [Each radius r]Hypotenuse. OP = Hypotenuse. OP [common]{tex}\\therefore{/tex}{tex}\\triangle{/tex}POQ\xa0{tex}\\cong{/tex}{tex}\\triangle{/tex}POR\xa0[By RHS rule]{tex}\\therefore{/tex} PQ = PR

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