IMO 1987 LL MON40

The perpendicular line issued from the center of the circum-

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IMO 1987 LL MON40

Origin: MON

Problem

The perpendicular line issued from the center of the circum- circle to the bisector of angle C in a triangle ABC divides the segment of the bisector inside ABC into two segments with ratio of lengths \lambda. Given b = AC and a = BC, find the length of side c.