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2013 ToT Fall Junior A p3 AN divides the bisector of angle C in half.

Source:

March 22, 2020
angle bisectorright trianglesemicirclegeometry

Problem Statement

Assume that CC is a right angle of triangle ABCABC and NN is a midpoint of the semicircle, constructed on CBCB as on diameter externally. Prove that ANAN divides the bisector of angle CC in half.
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