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ABC is congruent to triangle A'B'C'

Source: China TST 1992, problem 4

June 27, 2005
trigonometryratiorotationgeometry unsolvedgeometry

Problem Statement

A triangle ABCABC is given in the plane with AB=7,AB = \sqrt{7}, BC=13BC = \sqrt{13} and CA=19,CA = \sqrt{19}, circles are drawn with centers at A,BA,B and CC and radii 13,\frac{1}{3}, 23\frac{2}{3} and 1,1, respectively. Prove that there are points A′,B′,C′A',B',C' on these three circles respectively such that triangle ABCABC is congruent to triangle A′B′C′.A'B'C'.
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