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Math Help - math contest question

  1. #1
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    math contest question

    Given a circle with center O, PQ AND PR are two tangents from point P outside the circle. Prove that angle POQ = angle POR.
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  2. #2
    Super Member redsoxfan325's Avatar
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    Quote Originally Posted by shane99 View Post
    Given a circle with center O, PQ AND PR are two tangents from point P outside the circle. Prove that angle POQ = angle POR.
    So the triangles share a common hypotenuse PO. We know the two radii are congruent: OQ\cong OR. Since \angle PQO=90^o=\angle PRO (tangent lines to a circle form right angles with the radius), the two triangles are congruent by HL, and the two desired angles are congruent by CPCTC.
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