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ISL 1980 Problem 10

    Two circles C1C_{1} and C2C_{2} are (externally or internally) tangent at a point PP . The straight line DD is tangent at AA to one of the circles and cuts the other circle at the points BB and CC . Prove that the straight line PAPA is an interior or exterior bisector of the angle ∠BPC\angle BPC .

    Dataset text AI-MO AoPS. Quoted with source.

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