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An easy geometry about midpoints

Source: Indonesia National Math Olympiad 2021 Problem 2 (INAMO 2021/2)

November 8, 2021
geometrycircumcircle

Problem Statement

Let ABCABC be an acute triangle. Let DD and EE be the midpoint of segment ABAB and ACAC respectively. Suppose L1L_1 and L2L_2 are circumcircle of triangle ABCABC and ADEADE respectively. CDCD intersects L1L_1 and L2L_2 at M(M≠C)M (M \not= C) and N(N≠D)N (N \not= D). If DM=DNDM = DN, prove that △ABC\triangle ABC is isosceles.
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