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Консультация № 163909
01.04.2009, 18:50
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Здравствуйте, помогите, пожалуйста, решить задачу по геометрии, очень надо...
Величина одного из углов треугольника равна 20 градусов. Величина острого угла между биссектрисами двух других углов этого треугольника равна...
Величина одного из углов треугольника равна 20 градусов. Величина острого угла между биссектрисами двух других углов этого треугольника равна...
Обсуждение
01.04.2009, 19:23
общий
это ответ
Здравствуйте, Нос Татьяна Александровна!
Обозначим точки
A - вершина, угол при которой 20°
B и C - остальные вершины
О - точка пересечения биссектрис
[$8736$]A=20°
[$8736$]B+[$8736$]C=180-[$8736$]A=160[$186$] - через сумму углов треугольника ABC
[$8736$]CBO=[$8736$]B/2
[$8736$]BCO=[$8736$]C/2 - по определению биссектрисы
[$8736$]CBO+[$8736$]BCO=[$8736$]B/2+[$8736$]C/2=160[$186$]/2=80[$186$]
[$8736$]COB=180[$186$]-([$8736$]CBO+[$8736$]BCO)=180[$186$]-80[$186$]=100[$186$] - через через сумму углов треугольника ОBC
[$8736$]COB - тупой угол между биссектрисами. Острый угол является смежным ему и составляет 180[$186$]-[$8736$]COB=80[$186$]
Обозначим точки
A - вершина, угол при которой 20°
B и C - остальные вершины
О - точка пересечения биссектрис
[$8736$]A=20°
[$8736$]B+[$8736$]C=180-[$8736$]A=160[$186$] - через сумму углов треугольника ABC
[$8736$]CBO=[$8736$]B/2
[$8736$]BCO=[$8736$]C/2 - по определению биссектрисы
[$8736$]CBO+[$8736$]BCO=[$8736$]B/2+[$8736$]C/2=160[$186$]/2=80[$186$]
[$8736$]COB=180[$186$]-([$8736$]CBO+[$8736$]BCO)=180[$186$]-80[$186$]=100[$186$] - через через сумму углов треугольника ОBC
[$8736$]COB - тупой угол между биссектрисами. Острый угол является смежным ему и составляет 180[$186$]-[$8736$]COB=80[$186$]
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