4.6. Han(2; 3), B (-1; 2в отношении:​

Окружность касается сторон AB и AD прямоугольника ABCD и пересекает DC в единственной точке F, а BC-в точке E. 

Найти площадь AFCB, если AB=32, AD=40 и BE=1

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АBCD- прямоугольник. ⇒

AFCB - прямоугольная трапеция.  Площадь трапеции равна произведению полусуммы оснований  на высоту. 

S=0,5•(FC+AB)•BC

СF следует найти. 

Проведем радиусы ОК и ОТ к АВ и АД соответственно. 

АК=ОК=ОТ=ТА=R

Опустим из Е перпендикуляр ЕН на радиус ОК

КН=ВЕ=1⇒ НО=R-1

ЕН=ВК=АВ-R=32-R

По т.Пифагора из ∆ ОЕН

R²=(32-R)²+(R-1)²⇒

R²-66 R+1024=0  Решив квадратное уравнение, получим два корня:

R1=41;  R2=25

Первый не подходит, т.к. больше, чем АВ,  и будет касаться не АВ, а её продолжения. 

R=ОЕ=25

Проведем ОМ перпендикулярно СD. 

Основание СF=CM+MF

CM=BK=AB-R=7

MF=√(OF²-OM²)

OM=AD-R=40-25=15

MF=√(25²-15²)=20

CF=20+7=27

S=0,5•(27+32)•40=1180 ( ед. площади)

Progress Cheek 1 I variant 1.Complete the sentences in past perfect 1. When I came home, mother already (to cook) dinner. 2. When father returned from work, we already (to do) our homework. 3. When the teacher entered the classroom, the pupils already (10 open) their books. 4. Kate gave me the book which she (to buy) the day before 5. Nick showed the teacher the picture which he (to draw). 6. The boy gave the goats the grass which he (to bring) from the ficld 2. Write the sentences in the interrogative form and make general and who-questions. 1. Rose had written the letter by 7 о'clock yesterday. 2 Mrs Rogers had cooked the dinner by 6 о'clock last Sunday. 3. Jane and Ann had built the toy house by four o'clock yesterday. 3. Choose the right words to complete the sentences. 1) That day Jane felt so sad ahe could (ery/smile). 2) The puplls (ended/ finished) decorating the hall late in the afternoon. 3) Do you watch matehes of your favourite football (сrеw/teаm) on television? 4) We are playing basketball in the gyт, would you 1ike to joln (- /1in)? 5) No one liked the dish, we thought it was rather (Lasteful/tasteless). 6) In the I variant 1.Compleie the sentences in past рerfect b) hie