γεωμετρια α...

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    ,

    .

    , ,

    ,

    .

    . , , -

    , ,

    ,

    , ,

    .

    .

    , ,

    .

    : .

    12 :

    , .

    ,

    .

    .

    - .

    .

    ,

    , . ,

    , , ,

    .

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    ............................................................................................................ 7

    ....................................................................................................... 9

    2( )

    1: ................................................... 11

    2: - ........................................................................ 23

    3

    3: ................................................ . .............................. 35

    4: ...................... ............................... 55

    4

    5: .............................................. 69

    5

    6: ................................................................91

    7: .......................................................99

    8: ............................................111

    6

    9

    : ................................................................................137 10: .......................... 157

    7

    11: ............................................................175

    12:............................................................................185

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    2 o

    1o

    B

    A

    2 o

    -

    y

    x

    O

    A

    K

    B

    H

    x

    O

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    .

    : ,

    .

    i .

    (.

    (.)).

    i

    .

    , .. .. (.).

    i , -

    .

    -

    , , .

    1.

    .

    1 :

    1

    .

    :

    .

    .

    2

    ,

    .

    A

    BA

    1

    BA

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    14.

    2.

    -.

    .

    2 :

    3

    .

    A

    4

    .

    A

    3.

    . ( )

    A B

    B

    A

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    15.

    .

    x Ax .

    xA x

    x.

    .

    ,

    .

    A B

    .

    . . .

    .

    , ( ) .

    -

    .

    = .

    OA B

    = B

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    16.

    , -

    = .

    ) .

    , -

    .

    , .

    K Z

    B

    + = . .

    ) .

    , , -

    ,

    .

    , .

    Z

    A

    E

    - = . .

    ) .

    ,

    .

    1

    2,

    2

    3,

    3

    4,.,

    +1.

    -

    1

    + 1, ..

    A1 A2 A3 A A + 1

    B

    A

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    17.

    2

    1

    .

    .

    = 3x = 3.

    A x x

    x

    x B

    .

    1. , ,

    AB

    AM MB2

    .

    2. .

    .

    -

    .

    .

    .

    1

    , , ,

    . A

    M =2

    .

    A B

    M N

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    18.

    1

    ,A

    AM M2

    .

    ,

    2

    .

    (1),(2) A

    2 2 2 2

    .

    2

    = = = = :

    ( )2 2 2

    +

    = + = =

    2

    , , , ,

    . +

    i. = ii. + = + 2

    i.

    1

    ,A

    AM M2

    .

    ,

    2

    .

    2

    2 2 2 2 2

    2

    A B

    M N

    A B

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    19.

    i. = x = = y = , :

    2x 2y x y

    2 2

    ii. + = 2x + + + 2y = 2x + + 2y + = + .

    3

    , ,

    , . :

    -i. =

    2

    +ii. =

    2.

    ,A

    AM M

    2

    (1).

    i.

    2 2 2

    2

    2

    .

    ii.1 2

    2 2 2

    .

    4

    , , .

    3

    =4

    .

    . :3+ 4

    =7

    .

    K A

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    20.

    3 3 3= + = +

    3 4 4 4 4 4 4 3

    4= = = =

    3 47 3 4 7

    += + =

    5

    , , , = = ,

    . : ( ) ( ) ( )2 1 1

    = + .

    : ( ) ( )2 1 1

    = + .

    :( )

    ( )

    ( )

    ( )

    2

    + = .

    ( )

    ( )

    ( )

    ( )

    ( ) ( )

    ( )

    ( )

    ( )

    ( )

    ( )

    + +

    + = + = + =

    ( )( )( )

    ( ) ( )( )

    1 1 1 12

    + + + = + =

    .

    1. , , ,

    < .

    i. , < 2

    ii. , > 2.

    A M

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    21.

    2. , , , . 2 > .

    3. , , , ,

    .

    2

    , = + .

    4. , 5

    MA MB3

    = .

    , 5

    3

    = ,

    : ( ) ( ) ( )1 1 1

    = + .

    5. ,,, = 2 = 3.

    ,, ,

    = .

    .

    , , > > :

    + +

    < < 3

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