# Задачи по планиметрии С4 (многовариантные задачи)

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4 ( )

4( )

a, b, c , , , ( ). ,

2 . , . , , . . , . R r (Rr) R+r R-r .

. . . ( ) ( ). , ., , , .

- , ra - , a, S = (p-a)ra

R r , , , |cos B| , ,

2010 ABC =12, = 5, = 10. D , BD : DC = 4:9. , ADC ADB, AD F. EF. , , , , AD = d, BD = x, DC = . ADC

, D , , BD: DC = 4:9. , , .

D (.). ,

2. D (. ). = 4, = + = = 9. ,

D .. F AD, EF .:

CD ABCD CPD CD. , , 4. :AB=4,CP=PD,AK-.:

D , D:1. CD = 4, CP=PD=2. , =4, = =3. , = 6,

=

: , =

:

20.10.10 S 12 28 21. , , S.

, : , , N=9, ND=16, KD=16. OKD , OD=20. OKD HMD ,

MH = , DH = 8-, =3

, . = 15.

=

: 3

9.12.10 12. , , 13. , .

, . = 12, = 13, - , = 5, , =10.

, = =13, =121. =5, =8,

2.

:

(30 -2011) D AD N , BM:MN=1:3. , =6.

, M N , ==NC=CD=6. BM:MN=1:3, MN=18, =30. , BN=CM=6, =, MN=3x+3=6, =1,5, =7,5.: 30 7,5. (30 - 2011) 40, 15/17. , . , .

, . = . BD = 80. KN=2x, KD=x, LK=x. ABD LBP , ,

=16, , S=512.

, KN=x, KD=0,5x, LK=2x.

=20, S=800.

: 512 800.

(30 2011) , , 18, 5. , .

= a, = b, - , AC , - , . D , ,

b

=15, =19,5

5. , = 0,5 (19,52+15)=276.

: 18 11,25

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