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

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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, angle since these are between a tangent and a radius. From Pythagoras theorem,soand the triangles have three equal lengths so are congruent and angleandbisects

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