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locus of midpoints wanted, circle related

Source: 2014 Belarus TST 1.2

December 29, 2020
geometrymidpointLocus

Problem Statement

Given a triangle ABCABC. Let SS be the circle passing through CC, centered at AA. Let XX be a variable point on SS and let KK be the midpoint of the segment CXCX . Find the locus of the midpoints of BKBK, when XX moves along SS.
(I. Gorodnin)
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