Предмет: Геометрия, автор: orjabinina

На стороне AC треугольника ABC выбрана точка D такая, что AB=BD. Точка E на стороне BC такова, что ∠AEB=∠CED=69∘. Чему равен угол ABD?

Ответы

Автор ответа: siestarjoki

2

Рассмотрим треугольник AED и его описанную окружность.

Серединный перпендикуляр к стороне AD делит дугу AD пополам.

Биссектриса внешнего угла при вершине E также делит дугу AD пополам.

(Сумма углов A и D упирается на дугу AD. Половина внешнего угла - полусумма углов A и D - опирается на половину дуги AD.)

То есть серединный перпендикуляр к AD и биссектриса внешнего угла E пересекаются в точке B на описанной окружности.

∠ABD=∠AED=180-69*2=42°

Приложения:

siestarjoki: Лучше так:

siestarjoki: Хорда AD делит окружность на большую и меньшую дуги. Угол AED опирается на меньшую дугу, смежный угол равен 1/2 большей дуги => AEB, половина смежного угла равна 1/4 большей дуги и опирается на ее половину.

orjabinina: А где биссектриса внешнего угла?

siestarjoki: BC - биссектриса внешнего угла при вершине E треугольника AED

orjabinina: Спасибо.

Предыдущий вопрос

Следующий вопрос

Похожие вопросы

Предмет: Русский язык, автор: avatar4rus

Сочинение на тему: почему время называют лучшим лекарем?(350 слов и более)!

2 года назад

Предмет: Английский язык, автор: Аноним

Помогите написать текст на английском языке про Москву.
В тексте не больше 10 - 15 предложений! В тексте должно быть про темп жизни, про туристов, про население, про загрязнения и транспорт, про улицы, дома и мазагины, про экономику. Пожалуйста. SOS SOS SOS

2 года назад

Предмет: Английский язык, автор: frozen256

помогите решить тест очень срочно!!!
”13. A: “ Have you ever driven a really fast car ? ”
B: “ Yes, I _____ a Ferrari last year. It was great! ”

14. A: “ Could you _____ me where the post office is, please ? ”
B: “ It’s on the corner, opposite the cinema. ”

15. A: “ How often do you go to London ? ”
B: “ Not often. Three or four _____ a year. ”

16. A: “ Can your sister play the piano ? ”
B: “ Yes, very well. She’s _____ playing since she was seven. ”
17. A: “ I really love chocolate.
B: “ So _____ I .
”18. A: “ Can you come to a party tonight ? ”
B: “ I’m afraid not I have _____ study for my exam tomorrow.”

19. A: “ Can I help you with your bag ? ”
B: “ Oh, thank you. It’s much _____ heavy for me to carry. ”

20. A: “ This is the worst summer I can remember. ”
B: “ No, it isn’t. It’s ____ than last year. ”

21. A: “ What does your mother look ____ ? ”
B: “ She’s got short black hair and brown eyes. ”

22. A: “ In my opinion, the best whisky ____ made in Scotland. ”
B: “ Yes, I agree.
23. A: “ Have you seen the newspaper ? ”
B: “ It’s either on the table _____ in the magazine rack. ”

24. A: “ I can’t understand this exercise. ”
B: “ Keep trying. It’s not as difficult _____ you think. ”

25. A: “ Are you worried about the future ? ”
B: “ Well, I’m sure there ____ be some big changes in the next ten years.”

26. A: “ Would you like a cigarette ? ”
B: “ No, thanks. I gave ____ smoking two months ago. ”
27. A: “ What are you going to do this evening ? ”
B: “ If it _____ rain, we’ll probably go for a walk.”

28. A: “ Who discovered America ? ”
B: “ It ____ discovered by Columbus in 1492. ”

29. A: “ My dog, Billy, is very fat. ”
B: “ Yes. If he _____ less food, he would soon lose weight.”

30. A: “ Have you ____ a decision yet ? ”
A: “ Yes, we’re going to buy the new computer system. ”

31. A: “ Would you ____ if I opened the window ? ”
B: “ Good idea ! It’s very hot in here. ”

32. A: “ Is your father awake yet ? ”
B: “ He _____ be ! I can hear him singing in the bathroom. ”

33. A: “ Have you got any teddy bears? ”
B: “ Not now, but, as a child, I ____ to have three.”

34. A: “ Did you have a good journey ? ”
B: “ Yes, it only ____ three hours to get here. ”

35. A: “ What was wrong with Paul yesterday ? ”
B: “ Oh, he told me that he _____ had some bad news the previous day.”

36. A: “ You didn’t buy any carrots ! Did you forget ? ”
B: “ No, but there were ____ left in the shop. ”

37. A: “ Why was the teacher so angry with your class ? ”
B: “ It was because we ____ done our homework before the class.”

38. A: “ We have run ____ of paper for the photo-copier. ”
B: “ Then we’d better get some more at once. ”

39. A: “ Has your father recovered ____ his illness ? ”
B: “ Yes, he’s feeling much better now, thank you. ”

40. A: “ What do you think of Japanese food ? ”
B: “ Actually, this ____ the first time I’ve tried it. ”

41. A: “ Are you still having trouble with your car ? ”
B: “ No, I ____ it repaired last week. ”
42. A: “ Alice is ____ a good runner that she wins all her races. ”
B: “ Really ? Is she going to the Olympic Games ? ”

43. A: “ I’m planning to drive to Oxford this weekend. ”
B: “ Well, take a map in ____ you get lost. ”

44. A: “ I wish I ____ speak English perfectly ! ”
B: “ Honestly, most English people can’t do that ! ”

45. A: “ The crash wouldn’t have happened if I’d been more careful. ”
B: “ You mustn’t blame ____ . It wasn’t your fault. ”

46. A: “ ____ to some experts, global temperatures are rising. ”
B: “ I don’t believe it. It certainly isn’t very hot here. ”

47. A: “ I hope that this birthday card for Ali arrives on time. ”
B: “ You really ____ have posted it yesterday, as I told you. ”

48. A: “ Do you enjoy working in a big office ? ”
B: “ Not really. I hate ____ interrupted when I’m busy. ”

49. A: “ Did you start this job as soon as you left school ?
B: “ Yes. By December, I ____ have been working here for ten years. ”

50. A: “ The manager is in a very bad mood today. ”
B: “ Right, we’d ____ not make any more mistakes. ”

2 года назад

Предмет: Математика, автор: Nastya3000600

ДАЮ 15 БАЛЛОВ

36,8 - 3,5 × 1 1/7 ) : 1
16/25 - 14 13/15
С решением!!

8 лет назад

Предмет: Математика, автор: dam15cer

Какой наименьшой длины нужно сделать заготовки чтоб их можно было разрезать на бруски длиной 36см и 45см и 60см

8 лет назад