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Parallel Line Makes Tanget Circumcircle

Source: Iran Third Round 2013 - Geometry Exam - Problem 1

September 5, 2013
geometrycircumcirclegeometric transformationhomothetygeometry unsolved

Problem Statement

Let ABCDEABCDE be a pentagon inscribe in a circle (O)(O). Let BE∩AD=T BE \cap AD = T. Suppose the parallel line with CDCD which passes through TT which cut AB,CEAB,CE at X,YX,Y. If ω\omega be the circumcircle of triangle AXYAXY then prove that ω\omega is tangent to (O)(O).
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