MathDB

2

Part of 2008 Argentina Team Selection Test

Problems(1)

Circle + ratios

Source: Argentina IMO TST Problem 2

8/27/2009
Triangle ABC ABC is inscript in a circumference Γ \Gamma. A chord MN\equal{}1 of Γ \Gamma intersects the sides AB AB and AC AC at X X and Y Y respectively, with M M, X X, Y Y, N N in that order in MN MN. Let UV UV be the diameter of Γ \Gamma perpendicular to MN MN with U U and A A in the same semiplane respect to MN MN. Lines AV AV, BU BU and CU CU cut MN MN in the ratios 32 \frac{3}{2}, 45 \frac{4}{5} and 76 \frac{7}{6} respectively (starting counting from M M). Find XY XY
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