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geometry biimplication

Source: Indonesia IMO 2010 TST, Stage 1, Test 2, Problem 1

November 12, 2009
geometrytrapezoidcircumcirclegeometry proposed

Problem Statement

Let ABCD ABCD be a trapezoid such that AB∥CD AB \parallel CD and assume that there are points E E on the line outside the segment BC BC and F F on the segment AD AD such that \angle DAE \equal{} \angle CBF. Let I,J,K I,J,K respectively be the intersection of line EF EF and line CD CD, the intersection of line EF EF and line AB AB, and the midpoint of segment EF EF. Prove that K K is on the circumcircle of triangle CDJ CDJ if and only if I I is on the circumcircle of triangle ABK ABK. Utari Wijayanti, Bandung
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