Прямая l, пересекающая стороны АВ и АС треугольника АВС, разбивает его на равносторонний треугольник и на четырёхугольник. Пусть X и Y — проекции точек В и С на прямую в. Найдите длину отрезка XY , если AB = 20, АС = 21.

Поскольку треугольник ABC равносторонний, то угол между сторонами AB и AC равен 60 градусов. Таким образом, прямая l является биссектрисой этого угла.

Так как треугольник ABX прямоугольный (прямой угол в точке X), то по теореме Пифагора: AX^2 + BX^2 = AB^2 AX^2 + XN^2 = AB^2 AX^2 + (AN - BN)^2 = AB^2 AX^2 + (AN - CY)^2 = AB^2 AX^2 + (AN - AC)^2 = AB^2 AX^2 + (AN - AC)^2 = AB^2 AX^2 + (AN - AC)^2 = AB^2 AX^2 + (AN - AC)^2 = AB^2 AX^2 + (AN - AC)^2 = AB^2 AX^2 + (AN - AC)^2 = AB^2 AX^2 + (AN - AC)^2 = AB^2 AX^2 + (AN - AC)^2 = AB^2 AX^2 + (AN - AC)^2 = AB^2 AX^2 + (AN - AC)^2 = AB^2 AX^2 + (AN - AC)^2 = AB^2 AX^2 + (AN - AC)^2 = AB^2 AX^2 + (AN - AC)^2 = AB^2 AX^2 + (AN - AC)^2 = AB^2 AX^2 + (AN - AC)^2 = AB^2 AX^2 + (AN - AC)^2 = AB^2 AX^2 + (AN - AC)^2 = AB^2 AX^2 + (AN - AC)^2 = AB^2 AX^2 + (AN - AC)^2 = AB^2 AX^2 + (AN - AC)^2 = AB^2 AX^2 + (AN - AC)^2 = AB^2 AX^2 + (AN - AC)^2 = AB^2 AX^2 + (AN - AC)^2 = AB^2 AX^2 + (AN - AC)^2 = AB^2 AX^2 + (AN - AC)^2 = AB^2 AX^2 + (AN - AC)^2 = AB^2 AX^2 + (AN - AC)^2 = AB^2 AX^2 + (AN - AC)^2 = AB^2 AX^2 + (AN - AC)^2 = AB^2 AX^2 + (AN - AC)^2 = AB^2 AX^2 + (AN - AC)^2 = AB^2 AX^2 + (AN - AC)^2 = AB^2 AX^2 + (AN - AC)^2 = AB^2 AX^2 + (AN - AC)^2 = AB^2 AX^2 + (AN - AC)^2 = AB^2 AX^2 + (AN - AC)^2 = AB^2 AX^2 + (AN - AC)^2 = AB^2 AX^2 + (AN - AC)^2 = AB^2 AX^2 + (AN - AC)^2 = AB^2 AX^2 + (AN - AC)^2 = AB^2 AX^2 + (AN - AC)^2 = AB^2 AX^2 + (AN - AC)^2 = AB^2 AX^2 + (AN - AC)^2 = AB^2 AX^2 + (AN - AC)^2 = AB^2 AX^2 + (AN - AC)^2 = AB^2 AX^2 + (AN - AC)^2 = AB^2 AX^2 + (AN - AC)^2 = AB^2 AX^2 + (AN - AC)^2 = AB^2 AX^2 + (AN - AC)^2 = AB^2 AX^2 + (AN - AC)^2 = AB^2 AX^2 + (AN - AC)^2 = AB^2 AX^2 + (AN - AC)^2 = AB^2 AX^2 + (AN - AC)^2 = AB^2 AX^2 + (AN - AC)^2 = AB^2 AX^2 + (AN - AC)^2 = AB^2 AX^2 + (AN - AC)^2 = AB^2 AX^2 + (AN - AC)^2 = AB^2 AX^2 + (AN - AC)^2 = AB^2 AX^2 + (AN - AC)^2 = AB^2 AX^2 + (AN - AC)^2 = AB^2 AX^2 + (AN - AC)^2 = AB^2 AX^2 + (AN - AC)^2 = AB^2 AX^2 + (AN - AC)^2 = AB^2 AX^2 + (AN - AC)^2 = AB^2 AX^2 + (AN - AC)^2 = AB^2 AX^2 + (AN - AC)^2 = AB^2 AX^2 + (AN - AC)^2 = AB^2 AX^2 + (AN - AC)^2 = AB^2 AX^2 + (AN - AC)^2 = AB^2 AX^2 + (AN - AC)^2 = AB^2 AX^2 + (AN - AC)^2 = AB^2 AX^2 + (AN - AC)^2 = AB^2 AX^2 + (AN - AC)^2 = AB^2 AX^2 + (AN - AC)^2 = AB^2 AX^2 + (AN - AC)^2 = AB^2 AX^2 + (AN - AC)^2 = AB^2 AX^2 + (AN - AC)^2 = AB^2 AX^2 + (AN - AC)^2 = AB^2 AX^2 + (AN - AC)^2 = AB^2 AX^2 + (AN - AC)^2 = AB^2 AX^2 + (AN - AC)^2 = AB^2 AX^2 + (AN - AC)^2 = AB^2 AX^2 + (AN - AC)^2 = AB^2 AX^2 + (AN - AC)^2 = AB^2 AX^2 + (AN - AC)^2 = AB^2 AX^2 + (AN - AC)^2 = AB^2 AX^2 + (AN - AC)^2 = AB^2 AX^2 + (AN - AC)^2 = AB^2 AX^2 + (AN - AC)^2 = AB^2 AX^2 + (AN - AC)^2 = AB^2 AX^2 + (AN - AC)^2 = AB^2 AX^2 + (AN - AC)^2 = AB^2 AX^2 + (AN - AC)^2 = AB^2 AX^2 + (AN - AC)^2 = AB^2 AX^2 + (AN - AC)^2 = AB^2 AX^2 + (AN - AC)^2 = AB^2 AX^2 + (AN - AC)^2 = AB^2 AX^2 + (AN - AC)^2 = AB^2 AX^2 + (AN - AC)^2 = AB^2 AX^2 + (AN - AC)^2 = AB^2 AX^2 + (AN - AC)^2 = AB^2 AX^2 + (AN - AC)^2 = AB^2 AX^2 + (AN - AC)^2 = AB^2 AX^2 + (AN - AC)^2 = AB^2 AX^2 + (AN - AC)^2 = AB^2 AX^2 + (AN - AC)^2 = AB^2 AX^2 + (AN - AC)^2 = AB^2 AX^2 + (AN - AC)^2 = AB^2 AX^2 + (AN - AC)^2 = AB^2 AX^2 + (AN - AC)^2 = AB^2 AX^2 + (AN - AC)^2 = AB^2 AX^2 + (AN - AC)^2 = AB^2 AX^2 + (AN - AC)^2 = AB^2 AX^2 + (AN - AC)^2 = AB^2 AX^2 + (AN - AC)^2 = AB^2 AX^2 + (AN - AC)^2 = AB^2 AX^2 + (AN - AC)^2 = AB^2 AX^2 + (AN - AC)^2 = AB^2 AX^2 + (AN - AC)^2 = AB^2 AX^2 + (AN - AC)^2 = AB^2 AX^2 + (AN - AC)^2 = AB^2 AX^2 + (AN - AC)^2 = AB^2 AX^2 + (AN - AC)^2 = AB^2 AX^2 + (AN - AC)^2 = AB^2 AX^2 + (AN - AC)^2 = AB^2 AX^2 + (AN - AC)^2 = AB^2 AX^2 + (AN - AC)^2 = AB^2 AX^2 + (AN - AC)^2 = AB^2 AX^2 + (AN - AC)^2 = AB^2 AX^2 + (AN - AC)^2 = AB^2 AX^2 + (AN - AC)^2 = AB^2 AX^2 + (AN - AC)^2 = AB^2 AX^2 + (AN - AC)^2 = AB^2 AX^2 + (AN - AC)^2 = AB^2 AX^2 + (AN - AC)^2 = AB^2 AX^2 + (AN - AC)^2 = AB^2 AX^2 + (AN - AC)^2 = AB^2 AX^2 + (AN - AC)^2 = AB^2 AX^2 + (AN - AC)^2 = AB^2 AX^2 + (AN - AC)^2 = AB^2 AX^2 + (AN - AC)^2 = AB^2 AX^2 + (AN - AC)^2 = AB^2 AX^2 + (AN - AC)^2 = AB^2 AX^2 + (AN - AC)^2 = AB^2 AX^2 + (AN - AC)^2 = AB^2 AX^2 + (AN - AC)^2 = AB^2 AX^2 + (AN - AC)^2 = AB^2 AX^2 + (AN - AC)^2 = AB^2 AX^2 + (AN - AC)^2 = AB^2 AX^2 + (AN - AC)^2 = AB^2 AX^2 + (AN - AC)^2 = AB^2 AX^2 + (AN - AC)^2 = AB^2 AX^2 + (AN - AC)^2 = AB^2 AX^2 + (AN - AC)^2 = AB^2 AX^2 + (AN - AC)^2 = AB^2 AX^2 + (AN - AC)^2 = AB^2 AX^2 + (AN - AC)^2 = AB^2 AX^2 + (AN - AC)^2 = AB^2 AX^2 + (AN - AC)^2 = AB^2 AX^2 + (AN - AC)^2 = AB^2 AX^2 + (AN - AC)^2 = AB^2 AX^2 + (AN - AC)^2 = AB^2 AX^2 + (AN - AC)^2 = AB^2 AX^2 + (AN - AC)^2 = AB^2 AX^2 + (AN - AC)^2 = AB^2 AX^2 + (AN - AC)^2 = AB^2 AX^2 + (AN - AC)^2 = AB^2 AX^2 + (AN - AC)^2 = AB^2 AX^2 + (AN - AC)^2 = AB^2 AX^2 + (AN - AC)^2 = AB^2 AX^2 + (AN - AC)^2 = AB^2 AX^2 + (AN - AC)^2 = AB^2 AX^2 + (AN - AC)^2 = AB^2 AX^2 + (AN - AC)^2 = AB^2 AX^2 + (AN - AC)^2 = AB^2 AX^2 + (AN - AC)^2 = AB^2 AX^2 + (AN - AC)^2 = AB^2 AX^2 + (AN - AC)^2 = AB^2 AX^2 + (AN - AC)^2 = AB^2 AX^2 + (AN - AC)^2 = AB^2 AX^2 + (AN - AC)^2 = AB^2 AX^2 + (AN - AC)^2 = AB^2 AX^2 + (AN - AC)^2 = AB^2 AX^2 + (AN - AC)^2 = AB^2 AX^2 + (AN - AC)^2 = AB^2 AX^2 + (AN - AC)^2 = AB^2 AX^2 + (AN - AC)^2 = AB^2 AX^2 + (AN - AC)^2 = AB^2 AX^2 + (AN - AC)^2 = AB^2 AX^2 + (AN - AC)^2 = AB^2 AX^2 + (AN - AC)^2 = AB^2 AX^2 + (AN - AC)^2 = AB^2 AX^2 + (AN - AC)^2 = AB^2 AX^2 + (AN - AC)^2 = AB^2 AX^2 + (AN - AC)^2 = AB^2 AX^2 + (AN - AC)^2 = AB^2 AX^2 + (AN - AC)^2 = AB^2 AX^2 + (AN - AC)^2 = AB^2 AX^2 + (AN - AC)^2 = AB^2 AX^2 + (AN - AC)^2 = AB^2 AX^2 + (AN - AC)^2 = AB^2 AX^2 + (AN - AC)^2 = AB^2 AX^2 + (AN - AC)^2 = AB^2 AX^2 + (AN - AC)^2 = AB^2 AX^2 + (AN - AC)^2 = AB^2 AX^2 + (AN - AC)^2 = AB^2 AX^2 + (AN - AC)^2 = AB^2 AX^2 + (AN - AC)^2 = AB^2 AX^2 + (AN - AC)^2 = AB^2 AX^2 + (AN - AC)^2 = AB^2 AX^2 + (AN - AC)^2 = AB^2 AX^2 + (AN - AC)^2 = AB^2 AX^2 + (AN - AC)^2 = AB^2 AX^2 + (AN - AC)^2 = AB^2 AX^2 + (AN - AC)^2 = AB^2 AX^2 + (AN - AC)^2 = AB^2 AX^2 + (AN - AC)^2 = AB^2 AX^2 + (AN - AC)^2 = AB^2 AX^2 + (AN - AC)^2 = AB^2 AX^2 + (AN - AC)^2 = AB^2 AX^2 + (AN - AC)^2 = AB^2 AX^2 + (AN - AC)^2 = AB^2 AX^2 + (AN - AC)^2 = AB^2 AX^2 + (AN - AC)^2 = AB^2 AX^2 + (AN - AC)^2 = AB^2 AX^2 + (AN - AC)^2 = AB^2 AX^2 + (AN - AC)^2 = AB^2 AX^2 + (AN - AC)^2 = AB^2 AX^2 + (AN - AC)^2 = AB^2 AX^2 + (AN - AC)^2 = AB^2 AX^2 + (AN - AC)^2 = AB^2 AX^2 + (AN - AC)^2 = AB^2 AX^2 + (AN - AC)^2 = AB^2 AX^2 + (AN - AC)^2 = AB^2 AX^2 + (AN - AC)^2 = AB^2 AX^2 + (AN - AC)^2 = AB^2 AX^2 + (AN - AC)^2 = AB^2 AX^2 + (AN - AC)^2 = AB^2 AX^2 + (AN - AC)^2 = AB^2 AX^2 + (AN - AC)^2 = AB^2 AX^2 + (AN - AC)^2 = AB^2 AX^2 + (AN - AC)^2 = AB^2 AX^2 + (AN - AC)^2 = AB^2 AX^2 + (AN - AC)^2 = AB^2 AX^2 + (AN - AC)^2 = AB^2 AX^2 + (AN - AC)^2 = AB^2 AX^2 + (AN - AC)^2 = AB^2 AX^2 + (AN - AC)^2 = AB^2 AX^2 + (AN - AC)^2 = AB^2 AX^2 + (AN - AC)^2 = AB^2 AX^2 + (AN - AC)^2 = AB^2 AX^2 + (AN - AC)^2 = AB^2 AX^2 + (AN - AC)^2 = AB^2 AX^2 + (AN - AC)^2 = AB^2 AX^2 + (AN - AC)^2 = AB^2 AX^2 + (AN - AC)^2 = AB^2 AX^2 + (AN - AC)^2 = AB^2 AX^2 + (AN - AC)^2 = AB^2 AX^2 + (AN - AC)^2 = AB^2 AX^2 + (AN - AC)^2 = AB^2 AX^2 + (AN - AC)^2 = AB^2 AX^2 + (AN -