1999 USAMO Problems/Problem 6

Problem

Let $ABCD$ be an isosceles trapezoid with $AB \parallel CD$ . The inscribed circle $\omega$ of triangle $BCD$ meets $CD$ at $E$ . Let $F$ be a point on the (internal) angle bisector of $\angle DAC$ such that $EF \perp CD$ . Let the circumscribed circle of triangle $ACF$ meet line $CD$ at $C$ and $G$ . Prove that the triangle $AFG$ is isosceles.

Solution

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1999 USAMO (Problems • Resources)
Preceded by Problem 5	Followed by Last Question
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1999 USAMO Problems/Problem 6

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