Из вершин n и q параллелограмма mnpq, у которого mn≠np и угол м - острый, проведены перпендикуляры na и qb к диагонали mp. докажите, что четырехугольник naqb - параллелограмм

1. good weather makes me happy.does good weather make me happy? good weather doesn't make me happy. 2. irene helps her mother.does irene help her mother? irene doesn't help her mother.3. i take my dog out for a run every morning.do i take my dog out for a run every morning? i don't take my dog out for a run every morning. 4. she prefers tea to coffee.does she prefer tea to coffee? she doesn't prefer  tea to coffee. 5. students spend a lot of money on books.do students spend a lot of money on books? students don't spend a lot of money on books. 6. it takes a long time to become clever.does it take a long time to become clever? it doesn't take  a long time to become clever. 7. the chinese like spaghetti.do the chinese like spaghetti? the chinese don't like spaghetti. 8. old people like to wear t-shirts and jeans.do old people like to wear t-shirts and jeans? old people don't like to wear t-shirts and jeans. 9. he goes on business trips every month.does he go on business trips every month? he doesn't go on business trips every month. 10. it rains a lot in autumn.does it rain a lot in autumn? it doesn't rain a lot in autumn. 11. it seldom snows in the south of england.does it seldom snows in the south of england? it doesn't snow often in the south of england. 12. it takes me half an hour to get to my work.does it take me half an hour to get to my work? it doesn't take  me half an hour to get to my work. 13. she waters the flowers in her garden twice a week.does she water the flowers in her garden twice a week? she doesn't water  the flowers in her garden twice a week. 14. children enjoy playing computer games.do children enjoy playing computer games? children don't enjoy playing computer games. 15. i meet my classmates every year.do i meet my classmates every year? i don't meet my classmates every year. 16. we agree with you.do we agree with you? we don't agree with you.

Две стороны треугольника равны 3 и 5. Известно, что окружность, проходящая через середины этих сторон и их общую вершину, касается третьей стороны треугольника. Найдите третью сторону.

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АН и СН - касательные к окружности. 

АВ - секущая, АК - её внешняя часть. 

АВ=3, АК=0,5 АВ=1,5 

СВ - секущая, СМ - её внешняя часть

СВ=5, СМ=СВ:2=2,5

Квадрат касательной равен произведению секущей на её внешнюю часть.  ⇒

АН ²=АВ•AK=3*1,5=4,5=450/100

АН=√4,5=√(450/100)=√(9*25*2:100)=(3•5√2)/10=1,5√2

СН²=СВ•CM=5*2,5=1250/100

CH=√(25•25•2/100)=(25√2)/10=2,5√2

АС=АН+СН=1,5√2+2,5√2=4√2

Воспользуемся формулой площади треугольника
S=1/2*ab*sin С, где С - угол между сторонами а и b. Если углы треугольника обозначим как А, В, С, а стороны как а, b, c (соответственно 7, 9, 11), то получим
значения площади S=63/2*sin C=77/2*sin B=99/2*sin A.
Другая формула площади S=1/4*V(a+b+c)(a+b-c)(a+c-b)(b+c-a)=1/4V27*5*9*13=3/4V195.
63/2sin C=3/4*V195  => sin C=3/4*V195*2/63=3/126*v195=1/42V195
(cos C)^2=1-(sin c)^2  =>  (cos C)^2=1-195/1764=65/588  => cos C=V65/588=1/14*V65/3=1/42V195.
Аналогично находим cos B, cos A.