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Консультация № 188668
18.01.2016, 22:21
0.00 руб.
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1
Здравствуйте! Прошу помощи в следующем вопросе:
Не могли бы проверить?
В треугольнике ABC угол BAC равен 45(градусам), угол ACB равен 105 (градусам), AC=1, точка О-центр описанной окружности. Верны ли утверждения:
1) Точка О лежит вне треугольника ABC (да)
2) Угол COB - острый (да)
3)Радиус описанной около треугольника ABC окружности равен 1 (нет)
4)S(AOBC)=(√3+2)/2 (нет)
5)AB=(√6+√2)/2 (да)
Не могли бы проверить?
В треугольнике ABC угол BAC равен 45(градусам), угол ACB равен 105 (градусам), AC=1, точка О-центр описанной окружности. Верны ли утверждения:
1) Точка О лежит вне треугольника ABC (да)
2) Угол COB - острый (да)
3)Радиус описанной около треугольника ABC окружности равен 1 (нет)
4)S(AOBC)=(√3+2)/2 (нет)
5)AB=(√6+√2)/2 (да)
Обсуждение
19.01.2016, 09:10
общий
это ответ
Здравствуйте, Посетитель - 399097!
По-моему, Вы правильно ответили на вопросы 1, 4, 5.
2) В том, что угол COB - тупой, можно убедиться, если построить треугольник ABC и точку O. Кроме того, в треугольнике COB CO=BO=R=1, CB>1 (эта сторона в треугольнике ABC лежит против угла в 45[$186$], а AC=1 лежит против угла в 30[$186$]).
3) По теореме синусов
С уважением.
По-моему, Вы правильно ответили на вопросы 1, 4, 5.
2) В том, что угол COB - тупой, можно убедиться, если построить треугольник ABC и точку O. Кроме того, в треугольнике COB CO=BO=R=1, CB>1 (эта сторона в треугольнике ABC лежит против угла в 45[$186$], а AC=1 лежит против угла в 30[$186$]).
3) По теореме синусов
2R=AC/(sin 30[$186$])=1/(1/2)=2, R=1.
С уважением.
Об авторе:
Facta loquuntur.
Facta loquuntur.
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