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circumcenter of ABC lies on the line CL, median, bisector related

Source: Belarus TST 2009 6.1

June 13, 2020
geometryCircumcenterangle bisectormedian

Problem Statement

In a triangle ABC,AMABC, AM is a median, BKBK is a bisectrix, L=AM∩BKL=AM\cap BK. It is known that BC=a,AB=c,a>cBC=a, AB=c, a>c. Given that the circumcenter of triangle ABCABC lies on the line CLCL, find ACAC
I. Voronovich
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