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Locus of incenters of triangles

Source: Sharygin contest. The final raund. 2008. Grade 10. First day. Problem 4

August 31, 2008
geometryincentergeometry unsolved

Problem Statement

(A.Zaslavsky) Given three points C0 C_0, C1 C_1, C2 C_2 on the line l l. Find the locus of incenters of triangles ABC ABC such that points A A, B B lie on l l and the feet of the median, the bisector and the altitude from C C coincide with C0 C_0, C1 C_1, C2 C_2.
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