MathDB

6

Part of 1999 USAMO

Problems(1)

Isos Trap

Source: USAMO 1999 Problem 6

10/3/2005
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.
geometrytrapezoidgeometric transformationreflectionincentersymmetryIsosceles Triangle