# Math Help - math contest question

1. ## 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.

2. Originally Posted by shane99
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.