Thread: 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.

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 . We know the two radii are congruent: . Since (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.