MathDB
ABCD is a rhombus, M,N,K,L∈AB,BC,CD,DA and MN||LK

Source: Turkey TST 2000 P5

March 12, 2011
geometryrhombuscircumcircletrigonometryangle bisectorgeometry proposed

Problem Statement

Points M, N, K, LM,\ N,\ K,\ L are taken on the sides AB, BC, CD, DAAB,\ BC,\ CD,\ DA of a rhombus ABCD,ABCD, respectively, in such a way that MN∥LKMN\parallel LK and the distance between MNMN and KLKL is equal to the height of ABCD.ABCD. Show that the circumcircles of the triangles ALMALM and NCKNCK intersect each other, while those of LDKLDK and MBNMBN do not.
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