Proof That a Line Drawn From a Point to the Centre of a Circle Bisects the Angle Between the Two Tangents Drawn From That Point

The theorem is illustrated below.

Proof: Construct the trianglesandby drawing radii as below.

since both are radii of the circle andis common to both. Further, anglesince these are between a tangent and a radius. From Pythagoras theorem,soand the triangles have three equal lengths so are congruent and angleandbisects