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Консультация № 189678
11.08.2016, 12:31
0.00 руб.
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Уважаемые эксперты! Пожалуйста, помогите с решением и объяснением задачи №5 (а,б) :
Прикрепленные файлы:
Обсуждение
11.08.2016, 17:08
общий
это ответ
Здравствуйте, anton74551!
а)
Треугольники [$916$]ABC и A1B1C - подобны
AB/A1B1=AC/A1C=BC/B1C
Но из [$8895$]AA1C и [$8895$]BB1C косинус искомого угла
cos[$8736$]C=A1C/AC=B1C/BC
Таким образом
cos[$8736$]C=A1B1/AB=2[$8730$]3/4=[$8730$]3/2
[$8736$]C=30[$176$]
б) точки A, B1, A1 и B лежат на одной окружности (при том AB - её диаметр)
[$8736$]B1AA1=[$8736$]B1BA1 как вписанные, опирающиеся на одну дугу [$8745$]A1B1
Учитывая равенство углов при точке H, [$916$]AHB1 и [$916$]BHA1 - подобны
AH/HB1=BH/HA1
3HA1/3=4/HA1
HA12=4
HA1=2
AH=6
[$8736$]BAA1=[$8736$]BB1A1 как вписанные, опирающиеся на одну дугу [$8745$]A1B
Учитывая равенство углов при точке H, [$916$]AHB и [$916$]B1HA1 - подобны
AB/A1B1=AH/HB1=BH/HA1=2
Но, как мы установили в предыдущей части задачи,
cos[$8736$]C=A1B1/AB=1/2
[$8736$]C=60[$176$]
а)
Треугольники [$916$]ABC и A1B1C - подобны
AB/A1B1=AC/A1C=BC/B1C
Но из [$8895$]AA1C и [$8895$]BB1C косинус искомого угла
cos[$8736$]C=A1C/AC=B1C/BC
Таким образом
cos[$8736$]C=A1B1/AB=2[$8730$]3/4=[$8730$]3/2
[$8736$]C=30[$176$]
б) точки A, B1, A1 и B лежат на одной окружности (при том AB - её диаметр)
[$8736$]B1AA1=[$8736$]B1BA1 как вписанные, опирающиеся на одну дугу [$8745$]A1B1
Учитывая равенство углов при точке H, [$916$]AHB1 и [$916$]BHA1 - подобны
AH/HB1=BH/HA1
3HA1/3=4/HA1
HA12=4
HA1=2
AH=6
[$8736$]BAA1=[$8736$]BB1A1 как вписанные, опирающиеся на одну дугу [$8745$]A1B
Учитывая равенство углов при точке H, [$916$]AHB и [$916$]B1HA1 - подобны
AB/A1B1=AH/HB1=BH/HA1=2
Но, как мы установили в предыдущей части задачи,
cos[$8736$]C=A1B1/AB=1/2
[$8736$]C=60[$176$]
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