Вчетырехугольник abcd с диагоналями ас=7 и bd=12 вписана окружность радиуса 3. известно, что ab=ad. найдите площадь треугольника abd. решите !

1.если в четырехугольник вписана окружность и две стороны равны, то и другие две тоже равны. ( доказывается так же как доказывается теорема о том что если в четырехугольник можно вписать окружность, то суммы противолежащих сторон равны)

2. асперпендикулярна вд.( треугольники адс и абс равны по трем сторонам - значит ас - биссектриса, а т.к треугольник авд равнобедренный, то высота и медиана) отсюда

3 вд  точкой пересечения делится пополам. обозначим ее о. во=од=6

вспомним формулу площади четырехугольника - половина произведения диагоналей на синус угла между ними, а , т.к диагонали перпендикулярны, то половине произведения диагоналей, т.еsавсд= ас*вд/2=42.

4. площадь четырехугольника равна - произведению полупериметра на радиус вписанной окружности, т.е.(p/2)*r. (p/2)*3=42, (p/2)=14, p=28

5. ао=х, ос=(7-х)

6. по теореме пифагора находим ав и вс и помним, что их сумма равна полупериметру.

переносим один из корней в левую часть, возводим в квадрат, уничтожаются уничтожаются. еще раз разделяем на две стороны и возводим в квадрат

  уменя получилось уравнение

х=2,5 или х=4.5

находим площадь, учитывая. что диагонали взаимно перпендикулярны

12*2,5)/2=15 или (12+4,5)/2=27.

проверьте вычисленпия, могла ошибиться.

 

 

Essay on Sports
Hello, folks! Have you ever heard of this well-known saying: “A sound mind in a sound body"? I think the answer in most cases is “yes”. So, we’re discussing the importance of sports today.
Not so long ago sports was really important part of our day to day life. But with the rising popularity of television, the Internet and video games, sports and exercises are not so important anymore. There is a reason why we should do sports on daily basis. Going in for sports means to be energetic and healthy. While people who are not keen on it are often seen struggling with illnesses in their adulthood, such as diabetes, obesity etc; Moreover, it helps us not only to improve our body but our mind as well.
People who are good at sports also show a lifestyle of excellent quality. They are more active, can make better decisions and find the way out of stressful situations. Not encouraging children to take part in sports activities can make them lazy and peevish as they turn into grown-ups. Also, people who participate in sports competitions are more successful. It is a well-known fact that a man involved in sports activity from the very young age develops a very strong personality. He cultivates what is called the leadership.

Essay on Sports

Hello, folks! Have you ever heard of this well-known saying: “A sound mind in a sound body"? I think the answer in most cases is “yes”. So, we’re discussing the importance of sports today.

Not so long ago sports was really important part of our day to day life. But with the rising popularity of television, the Internet and video games, sports and exercises are not so important anymore. There is a reason why we should do sports on daily basis. Going in for sports means to be energetic and healthy. While people who are not keen on it are often seen struggling with illnesses in their adulthood, such as diabetes, obesity etc; Moreover, it helps us not only to improve our body but our mind as well.

People who are good at sports also show a lifestyle of excellent quality. They are more active, can make better decisions and find the way out of stressful situations. Not encouraging children to take part in sports activities can make them lazy and peevish as they turn into grown-ups. Also, people who participate in sports competitions are more successful. It is a well-known fact that a man involved in sports activity from the very young age develops a very strong personality. He cultivates what is called the leadership.