Download - Ma Thematic A - 130 Problems in Geometry

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= 90

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. ==90 . = = = = = = ---> //. ) // ( ) =/2 (1) , =/2 (2) ( ) =/2 (3) 1,2,3 =(++)/2

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= 20 (-3) (=) = 20 . , = 60 = 50 . . .

= 20O = ( = = 50 ) = = = 60O (==) = 40O = == = 70O

= 40 = 30O

2

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(2),(3) (1)

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http://www.mathematica.gr/forum/viewtopic.php?f=27&t=261 (=90), G . , .

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1 , = . 3 3 2 2 2 2 = = , : 2 = = , 3 3 3 3 3 = (1) 3 . =

2 ++ + = = = = 2 3 3 3 2 2 = 2 2 = ( + )( ) = 2 ( ) = 2 ( ) (3) , : = (2)

(2)

5 4 + + 5 4 3 = 2 (2) (3) : = = , = 3 2 3 3: = = 2

3 3 4 3 5 3 2 = = = , = 3 2 2 3 2 3 2

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http://www.mathematica.gr/forum/viewtopic.php?f=20&t=1757 (.2-3), 1990, . 1. ( = ) , .A

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20 30

140 10 40

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30 140 50 . : = 80

, : 30 80 80 80 80 = = = = =1, 140 50 2140 50 90 190 10

= , = = 70 .

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F Q H P

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49 http://www.mathematica.gr/forum/viewtopic.php?f=20&t=529

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C , D : = 50 C = 100 .

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1 2 40 240 : x + y = + = ... = 1 , (PC) = 1, DPC 2 2 1 + 40 1 + 40 2 0 2 0

2

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40 DC. D 2 80 1 1 1 1 1+ + 80 = = 2 2 2 80 280 1 2 : ( x + 1) + y2 = 42 80 xx ( x0 , 0) .

(DA) = (PA) =

2

2

1 1 x0 + 1 = 2 4 80 280 1 1, 0 , D xx. 280 (D) = (DB) DA = DA = 50 AP= 30 .

: ( x0 + 1) + 02 =2

ABCD, . PBC= 30 . x 30. , , B :PB = 30 P = 70

. :1 1 PB P P 1 280 P = 280 = = 70 30 70 30 270 80 30 1 1 10 10 2 2 = = =1 60 80 1 10 2

() = (C) = 1, , C , C, PBC= 30 , ...

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