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CZ-SK-MO 2008 Problem 2

    Two disjoint circles W1(S1,r1)W_1(S_1,r_1) and W2(S2,r2)W_2(S_2,r_2) are given in the plane. Point AA is on circle W1W_1 and AB,ACAB,AC touch the circle W2W_2 at B,CB,C respectively. Find the loci of the incenter and orthocenter of triangle ABCABC .

    Dataset text AI-MO AoPS. Quoted with source.

    Official text: Czech-Slovak Mathematical Olympiad 2008 official paper, page 4.

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