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concurrency starting with the symmetric points of an interior wrt midpoints

Source: Czech-Polish-Slovak Junior Match 2012, Individual p1 CPSJ

March 11, 2020
concurrencyconcurrentsymmetrymidpointsgeometry

Problem Statement

Point PP lies inside the triangle ABCABC. Points K,L,MK, L, M are symmetrics of point PP wrt the midpoints of the sides BC,CA,ABBC, CA, AB. Prove that the straight AK,BL,CMAK, BL, CM intersect at one point.
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