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circumcentre of a triangle is the incentre of another

Source: CRMO 2014 region 2 p1

September 29, 2018
geometrycircumcircleincenterperpendicular bisector

Problem Statement

In an acute-angled triangle ABC,∠ABCABC, \angle ABC is the largest angle. The perpendicular bisectors of BCBC and BABA intersect AC at XX and YY respectively. Prove that circumcentre of triangle ABCABC is incentre of triangle BXYBXY .
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