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forum.virtualchallengemeets.com • View topic - USAMO 2007 Problem 6

USAMO 2007 Problem 6

Pose Olympiad-level questions to the monkeys in the peanut #.

USAMO 2007 Problem 6

Postby zefuri » Wed Apr 25, 2007 5:49 pm

Let [unparseable or potentially dangerous latex formula] be an acute triangle with ω, Ω, and [unparseable or potentially dangerous latex formula] being its incircle, circumcircle, and circumradius, respectively. Circle ω_A is tangent internally to Ω at [unparseable or potentially dangerous latex formula] and tangent externally to ω. Circle Ω_A is tangent internally to Ω at [unparseable or potentially dangerous latex formula] and tangent internally to ω. Let [unparseable or potentially dangerous latex formula] and [unparseable or potentially dangerous latex formula] denote the centers of ω_A and Ω_A, respectively. Define points [unparseable or potentially dangerous latex formula] analogously. Prove that

[unparseable or potentially dangerous latex formula]

with equality if and only if triangle [unparseable or potentially dangerous latex formula] is equilateral.
zefuri
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