IMO 1992 LL IRN37

Let the circles C1, C2, and C3 be orthogonal to the circle C

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IMO 1992 LL IRN37

Origin: IRN

Problem

Let the circles C1, C2, and C3 be orthogonal to the circle C and intersect each other inside C forming acute angles of measures A, B, and C. Show that A + B + C < \pi.