MathDB
Isos Trap

Source: USAMO 1999 Problem 6

October 3, 2005
geometrytrapezoidgeometric transformationreflectionincentersymmetryIsosceles Triangle

Problem Statement

Let ABCDABCD be an isosceles trapezoid with AB∥CDAB \parallel CD. The inscribed circle ω\omega of triangle BCDBCD meets CDCD at EE. Let FF be a point on the (internal) angle bisector of ∠DAC\angle DAC such that EF⊥CDEF \perp CD. Let the circumscribed circle of triangle ACFACF meet line CDCD at CC and GG. Prove that the triangle AFGAFG is isosceles.
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