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AD = AO wanted, 2 circles and angle bisector related

Source: Switzerland - Swiss ΜΟ 2017 p1

July 14, 2020
geometryangle bisectorcirclesequal segments

Problem Statement

Let AA and BB be points on the circle kk with center OO, so that AB>AOAB> AO. Let CC be the intersection of the bisectors of ∠OAB\angle OAB and kk, different from AA. Let DD be the intersection of the straight line ABAB with the circumcircle of the triangle OBCOBC, different from BB. Show that AD=AOAD = AO .
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