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1

Part of 1992 China Team Selection Test

Problems(2)

16 students took part in a competition

Source: China TST 1992, problem 1

6/27/2005
16 students took part in a competition. All problems were multiple choice style. Each problem had four choices. It was said that any two students had at most one answer in common, find the maximum number of problems.
combinatoricscombinatorics solvedProbabilistic Methoddouble countingChinaChina TSTmaximum
ABC is congruent to triangle A'B'C'

Source: China TST 1992, problem 4

6/27/2005
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'.
trigonometryratiorotationgeometry unsolvedgeometry