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angle chasing, given angle bisectors and circumcircles

Source: 2006 Estonia National Olympiad Final Round grade 10 p3

March 12, 2020
geometryangle bisectorAngle Chasingcircumcircle

Problem Statement

Let AG,CHAG, CH be the angle bisectors of a triangle ABCABC. It is known that one of the intersections of the circles of triangles ABGABG and ACHACH lies on the side BCBC. Prove that the angle BACBAC is 60o60 ^o
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