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concurrent, 4 right angles related

Source: 2022 South Russian Girls MO - Assara Seniors p3

March 1, 2024
geometryconcurrencyconcurrent

Problem Statement

In a convex quadrilateral ABCDABCD, angles BB and DD are right angles. On on sides ABAB, BCBC, CDCD, DADA points KK, LL, MM, NN are taken respectively so that KN⊥ACKN \perp AC and LM⊥ACLM \perp AC. Prove that KMKM, LNLN and ACAC intersect at one point.
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