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ASU 182 All Soviet Union MO 1973 similar triangles on sides of triangle

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July 4, 2019
geometrysimilar trianglesconcurrent

Problem Statement

Three similar acute-angled triangles AC1B,BA1CAC_1B, BA_1C and CB1ACB_1A are constructed on the outer side of the acute-angled triangle ABCABC. (Equal triples of the angles are AB1C,ABC1,A1BCAB_1C, ABC_1, A_1BC and BA1C,BAC1,B1ACBA_1C, BAC_1, B_1AC.)
a) Prove that the circles circumscribed around the outer triangles intersect in one point.
b) Prove that the straight lines AA1,BB1AA_1, BB_1 and CC1CC_1 intersect in the same point
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