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2002 AMC 10BProblem 22P21-25~4 minPrint
Triangles: Area & PythagoreanSystems of EquationsSet up the equation/formula and compute; no special trick neededExploit symmetry to reduce work or pair up objects

Let △XOY\triangle XOY be a right-angled triangle with m∠XOY=90∘m\angle XOY = 90^{\circ} . Let MM and NN be the midpoints of legs OXOX and OYOY , respectively. Given that XN=19XN = 19 and YM=22YM = 22 , find XYXY .

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Problem © Mathematical Association of America (MAA), American Mathematics Competitions. Reproduced for non-commercial educational use. Solution and commentary are original to this site. Also appeared as 2002 12B #20.