Предмет: Геометрия, автор: ivanivanov6512

В остроугольном треугольнике ABC сторона АВ = 8, ВС = 6. Высоты AL и СК пересекаются в точке Р. Через точки А и Р проведены прямые, перпендикулярные прямой KL и пересекающие прямую ВС соответственно в точках Н и Т. Найдите длину отрезка ТН.

Ответы

Автор ответа: Аноним

2

Достроим треугольник АВС до параллелограмма ABCE. Высоты треугольника AL и CK также являются высотами параллелограмма.

EP ⊥ KL ⇒ точки E, P, F, T лежат на одной прямой. Так как AH ⊥ KL и PT ⊥ KL, то AH ║ PT и следует обратить внимание на то что четырёхугольник AEHT - параллелограмм, значит TH = AE = BC = 6

Ответ: 6.

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