# ΚΕΦΑΛΑΙΟ 10Ο 10 - panepistimiaka- ?ΑΝΑΓΟΠΟΥΛΟΣ ΑΝΤΩΝΗΣ – ΜΑΘΗΜΑΤΙΚΟΣ – Β’ ΛΥΚΕΙΟΥ ΓΕΩΜΕΤΡΙΑ Σελίδα 1 ΚΕΦΑΛΑΙΟ

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• 1

10

10.4

1 , .

, : 2

+ += .

, : ( )( )( ) = .

9.4 ( 2) 2 ( )( )( ) = ,

: 1 1 2 ( )( )( ) ( )( )( )2 2

= = = .

2 . : = . ( , ). , , , : ( ) ( ) ( ) ( ) = = + +

1 1 1 1 1( ) 22 2 2 2 2 = + + = + + = = .

3 R

. : 4R

= .

5 8.2, : 2R = .

: 1 12 2 2 4R R

= = = .

4 ( ) :

1 1 12 2 2 = = = .

= .

90 < , :

= = =

.

• 2

90 > , :

1 (180 )

= = =

.

= . 90 = , 90 = = = .

1

: 2R

= = =

.

: 12 =

4R

= , :

1 22 4 2

RR R

= = =

. :

2R

=

2R

=

, .

2 = 13, = 14 = 15. : () , () , () , () .

() : 13 14 15 42 212 2 2

+ + + += = = = .

: ( )( )( ) 21(21 13)(21 14)(21 15) = =

21 8 7 6 84= = .

() : 1 1 16884 132 2 13 = = = . :

1 184 14 122 2 = = = 1 1 5684 15

2 2 5 = = = .

() : 84 21 4 = = = .

: 13 14 15 13 14 15 65844 4 84 4 8

R RR R

= = = =

.

() : 132

= , 7 = 152

= . :

13 157 212 22 2

+ +

= = . : ( )( )( ) =

221 21 13 21 14 21 15 21 74 3 21 7 3 21 212 2 2 2 2 2 2 2 2 = = = = =

.

• 3

1

: 12 = , : 1

2 .

;

2 () = 9 = 1,5. ;

3 , 6 = , 4 = 30 = . : () , () .

4 , 8 .., 2 =

150 = . .

5 , 10 = , 12 = 14 = . : () , () () .

6 , 4 = , 7 = 60 = . .

7 ( 90 = ), 6 = 8 = . : () , () , () .

8 , 1 = = 3 = . : () , () , () = .

9 , , 4 = . : () , () , () = .

• 4

10 , 6 = , 4 = 6 3 = .. : () , () , () .

11 , 12 = , 4 = 60 = . : () , () , () .

12 : = , : 90

= .

13 , , , : (i) ( ) 90 < < , (ii) ( ) 90 = = , (iii) ( ) 90 > > .

14

: ( )( )

=

.

15 . = , = ,

= = , :

+=

+.

16 30 .

: ( )4

= .

17 ,

:

=

+ +.

• 5

18 = . 1,R R 2R , , : 1 2R R R = = .

19 , 60 = , .

: 3 1 1

= + .

20

, , : 21 1

+ =

.

: () 2 + = ,

() 6

R = , R

, , ,

() 1 1 2

+ = .

21 , 5 = , 12 = , 13 = . () : 90 = , () . () , () , .

22 , 14 = , 12 = 24 10 = ., 10 = . : () , () , () , () .

23 , 1 2 = + , 2 =

2( )4

= .

() 3 , () R , () .

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