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

Embed Size (px)

Text of ΚΕΦΑΛΑΙΟ 10Ο 10 - panepistimiaka- ?ΑΝΑΓΟΠΟΥΛΟΣ ΑΝΤΩΝΗΣ –...

  • 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 , () .