Предмет: Геометрия, автор: Аноним

в остроугольном треугольнике abc проведена высота bh и биссектриса ad пересекающиеся в тоске о.Оказалось что угол АОВ в четыре раза больше угла DAB.Чему равен угол САВ

Ответы

Автор ответа: volodyk

треугольник АВС, ВН-высота, АД-биссектриса, уголДАВ=уголДАВ=х, уголАОВ=4х, треугольник АОВ, уголАВО=180-уголДАВ-уголАОВ180-х-4х=180-5х, треугольник АВН прямоугольный, уголАВО=90-2*уголДАВ=90-2х, 180-5х=90-2х, 3х=90, х=30угол САВ=2*30=60

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