MathDB

2

Part of 2000 Turkey Team Selection Test

Problems(1)

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

Source: Turkey TST 2000 P5

3/12/2011
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.
geometryrhombuscircumcircletrigonometryangle bisectorgeometry proposed