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Miklós Schweitzer 1954- Problem 10

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September 29, 2015
geometrycollege contests

Problem Statement

10. Given a triangle ABCABC, construct outwards over the sides AB,BC,CAAB, BC, CA similiar isosceles triangles ABC1,BCA1ABC_{1}, BCA_{1} and CAB1CAB_{1}. Prove that the straight lines AA1.BB1AA_{1}. BB_{1} and CC1CC_{1} are concurrent. Is this statemente true in elliptic and hyperbolic geometry, too? (G. 19)
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