IMO Shortlist 1979 problem 24


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2. travnja 2012.
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A circle C with center O on base BC of an isosceles triangle ABC is tangent to the equal sides AB,AC. If point P on AB and point Q on AC are selected such that PB \times CQ = (\frac{BC}{2})^2, prove that line segment PQ is tangent to circle C, and prove the converse.
Izvor: Međunarodna matematička olimpijada, shortlist 1979