MathDB

11

Part of 2009 Sharygin Geometry Olympiad

Problems(1)

Given a quadrilateral

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

5/31/2009
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.
geometrycircumcircletrapezoidnumber theoryleast common multiplegeometry proposed