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angle chasing with touchpoints from incircle and excirles

Source: Sharygin 2010 Final 9.5

October 6, 2018
geometryincircleAngle Chasingexcircle

Problem Statement

The incircle of a right-angled triangle ABCABC (∠ABC=90o\angle ABC =90^o) touches AB,BC,ACAB, BC, AC in points C1,A1,B1C_1, A_1, B_1, respectively. One of the excircles touches the side BCBC in point A2A_2. Point A0A_0 is the circumcenter or triangle A1A2B1A_1A_2B_1, point C0C_0 is defined similarly. Find angle A0BC0A_0BC_0.
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