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three sides of which are equal to BM, MN, ND

Source: Vietnam TST 1994 for the 35th IMO, problem 1

June 25, 2005
geometryparallelogramcircumcirclegeometry unsolved

Problem Statement

Given a parallelogram ABCDABCD. Let EE be a point on the side BCBC and FF be a point on the side CDCD such that the triangles ABEABE and BCFBCF have the same area. The diaogonal BDBD intersects AEAE at MM and intersects AFAF at NN. Prove that: I. There exists a triangle, three sides of which are equal to BM,MN,NDBM, MN, ND. II. When E,FE, F vary such that the length of MNMN decreases, the radius of the circumcircle of the above mentioned triangle also decreases.
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