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Given a quadrilateral

Source: I.F.Sharygin contest 2009 - Correspondence round - Problem 11

May 31, 2009
geometrycircumcircletrapezoidnumber theoryleast common multiplegeometry proposed

Problem Statement

Given quadrilateral ABCD ABCD. The circumcircle of ABC ABC is tangent to side CD CD, and the circumcircle of ACD ACD is tangent to side AB AB. Prove that the length of diagonal AC AC is less than the distance between the midpoints of AB AB and CD CD.
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