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intersection point of internal common tangent lies on angle bisector

Source: 2013 Oral Moscow Geometry Olympiad grades 10-11 p2

August 16, 2019
common tangentsinscribed circlesangle bisectorequal anglesgeometry

Problem Statement

Inside the angle AODAOD, the rays OBOB and OCOC are drawn such that ∠AOB=∠COD.\angle AOB = \angle COD. Two circles are inscribed inside the angles ∠AOB\angle AOB and ∠COD\angle COD . Prove that the intersection point of the common internal tangents of these circles lies on the bisector of the angle AODAOD.
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