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Indian Team Selection Test 2010 ST3 P1

Source:

May 22, 2010
geometrycircumcirclegeometric transformationdilationreflectionparallelogramangle bisector

Problem Statement

Let ABCDABCD be a cyclic quadrilaterla and let EE be the point of intersection of its diagonals ACAC and BDBD. Suppose ADAD and BCBC meet in FF. Let the midpoints of ABAB and CDCD be GG and HH respectively. If Γ\Gamma is the circumcircle of triangle EGHEGH, prove that FEFE is tangent to Γ\Gamma .
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