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Треугольники

Треугольники

Помогите, пожалуйста решить задачу:
Задача №1Дан треугольник с углом 120 градусов. Проведены биссектрисы. Доказать, что если соединить их основания, то получится прямоугольный треугольник.

Заранее благодарен.
#1
Задача №2Точка Р лежит на стороне ВС `Delta АВС` Известно что ВР=16 РС=9 `/_АВС=30^@ /_ВАР=/_АСВ` Найдите площадь `Delta АВР`


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#2
Задача №3Треугольник АВС равнобедренный,АВ=ВС=9 и АС=14. найти
а)расстояние между точкой пересечения медиан и точкой пересечения биссектрис
б)расстояние от центра описанной окружности до стороны АС

Помогите,пожалуйста,совсем запуталась в маленьких треугольниках
#3
Задача №4Окружность, проходящая через середину катета ВС и середину гипотенузы АВ прямоугольного треугольника АВС, касается катета АС в точке К. Найти соотношение СК:АК.

СПАСИБО! :) :)
#4
Задача №5ДВе медианы равнобедренного треугольника взаимно перпендикулярны. Боковая сторона равна корень из 10. Найдите площадь треугольника.
#5
Уважаемые математики и любители! Помогите пожалуйста решить задачу -
Задача №6В прямоугольном треугольнике АВС, угол C=90º, разность длин медианы СM и высоты СK равна 7, периметр треугольника равен 72. Найти длину гипотенузы.
#6
Задача №7Прямая, проходящая через вершину A равностороннего треугольника ABC со стороной 6, перпендикулярна стороне AB . На этой прямой выбрана точка D так, что AD в два раза больше высота треугольника ABC. Отрезок DE, соединяющий точку D c cерединой AB, пересекает сторону AC в точке F. Найти длину FE.
#7
Задача №8В треугольнике ABC к стороне BC проведена медиана AD. Найти длину стороны BC, если ` /_ А= 60 ^@ `, AD=2`sqrt 11`, полупериметр равен 10.
#8
Задача №9В равнобедренном треугольнике АВС (АВ=ВС) проведены биссектриса АР и высота СQ, точка их пересечения обозначена М. Площади треугольников АМС и АВС относятся как 9:20. Найдите sinBАC.
#9
помогите решить!
Задача №10в ТРЕУГОЛЬНИКЕ УГЛЫ РАВНЫ 45,45,90 градусов.Длина между углами 45 и 45 равна 1 метр.Найти длины сторон


!
Отредактируйте свое сообщение в соответствии с правилами. ~Ice
#10
Здравствуйте подскажите пожалуйста
Задача № 11Докажите, что наибольшую площадь из всех треугольников имеет равносторониий треугольник
я не как не могу что то додуматься как это доказать...если у нас есть окружность с фиксированным радиусом то логично что наибольшая будет у равносторонеего...а если нет окружности...как ...что то я запуталась подскажите пожалуйста..спасибо
#11
Задача № 12В прямоугольном треугольнике `АВС` из вершины прямого угла С проведены биссектрисса `СL` и медиана `CM` .Найдите площадь треугольника `АВС` если `LM` = `a` , `CM` = `b` .


Эта задача из сборника Гордина "Задача С4" подскажите как тут решить пожалуйста а то у меня не получается...
#12
Задача№13В прямоугольном треугольнике АВС ( < C = 90 ) проведены высота `СD` и медиана `CE`. Площади треугольников `ABC` и `CDE` равны соответственно 10 и 3 найдите АВ


У меня тоже мленьки вопрос и этой книжечи Гордина по С4
ТУт получается один треугольник разбивается н ти маленьких площади их 5, 3 , 2. а какдальше решить? ведь нс нет не одной длины...я из площадей выражаа выражала...но получается одно уравнние с двумя незвесными...подскажит как решить пожалуйста
#13
Задача №14Вне пряоугольного треугольника `АВС` на его катетах АС и ВС построены квадраы `ACDE` и `BCFG`. продолжение медианы `СМ` треугольника АВС пересекает прямую `DF` в точке `N` . найдите отрезок `CN` если катеты равны 1 и 4

Я искала в нигме эту заачку ...нету...
Задачка тоже из ГОрдина по С4
подскжите пожалуйста я не как не могу понять...у нас получается она в одно действие...данный треугольник АВС и треугольник образованный сторонами квадратов равны....а значит и равны в них все элемены. .. достаточно найти медиану СМ и она будет равна CN но что то видемо не правильно так как с ответом не сходится..помогите пожалуйста
#14
Задача №15треугольник АВС прямоугольный,угол С=90. Через середину катета АС -точку М проведена прямая,пересекающая гипотенузу АВ в точке D и продолжение стороны ВС в точке К. Известно,что около четрыхугольника СМDВ можно описать окружность и КМ = 3,МD =2. Найти радиус окружности и расстояние от точки В до прямой АК.

Пока я нашла только,что угол КDВ=90,КD=5. подскажите как дальше
вот мой рисунок | +
Изображение


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