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Prove that A+B+C < pi

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September 2, 2010
geometrycirclesTrigonometric inequalityanglesIMO ShortlistIMO Longlist

Problem Statement

Let the circles C1,C2C_1, C_2, and C3C_3 be orthogonal to the circle CC and intersect each other inside CC forming acute angles of measures A,BA, B, and CC. Show that A+B+C<π.A + B +C < \pi.
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