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13center2bprob

13center2bprob
13center2bprob

[1] O 2 A (6,0), B(3,3) , AB 2:1 P, 1:2 Q 3 O, P, Q C (1) P ( , ) ,

Q ( , ) (2) C OP , OP , y = x + , PQ , PQ , y x =?

2 C , C

(x ? )(2y ++ )2

=

(3) C x 2 , O R , R OA

:1

[2]

( ) 3x y z ++=, 352222x y z ++=, 4911116222x y z

+

+= x , y , z ,

x y z

2x X =, 2y Y =, 2z Z = , x y z X Y Z ( ) , X , Y , Z

XYZ = , 352X Y Z ++=

, XY YZ ZX ++=

,

t 3 ()()()t X t Y t Z ???

()()()t X t Y t Z ???32()()t X Y Z t XY YZ ZX t XYZ =?+++++? 3

t =?

()(12

t t =?? )(t ? ) , X Y Z , 12

X =, Y = , Z = ,

log x X =, log y Y =, log z Z =

x = , y = , z =

a ,

x ()x f , 323()3x x a x a =?+f ()y x =f , x = a , x =

a

, 2 ( , )a

, (

, )

a

y = 2x ? a

x

C C l

y = a

x

, l m

y =

x C

y =? 2x + a

x

D D l S , S =

C m x , 0a

C m

T S T = a

=

, ,

S =

(1) {}n p

13p =, 1113

n n p p +=+ (1,2,3,)n =!

{}n p , n ,

()113n n p p +?

=?

(1,2,3,)n =!

, {}n p ,

2

1

n n p ?=

+

?

, n

1

n

k k p =∑(

)

1

1n

n =

?

+

(2) {}n a , 3 13a =, 23a =, 33a = , n

1

32

n n n n a a a a ++++=

, {}n b , {}n c , n , 21n n b a ?=,

2n n c a = {}n b , {}n c ,

12

43

a a a a +== , 53a =, 6a =

, 73a =

, 12343b b b b ==== ,

3n b = (1,2,3,)n =!

, 13b = , n ,

1n n b b +=

, 1n = , , n k = , 1n k =+ , 1

[ ] 1n = , 13b =, 23b =

[ ] n k = , ,

1k k b b +=

1n k =+ , n 2k , 21k ?

21

k

k b ++=

, 11

k k c ++=

, 2k b +

2k k k

b +=

, , 21k k b b ++= , 1n k =+

[ ], [ ] , n , , {}n b 3n b = , n 21n ?

1113

n n c c +=+ (1,2,3,)n =!

, 1c = , {}n c , (1)

{}n p

OA 5=, OC 4=, AOC θ∠= OABC , OA 3:2 D , A BD OC E , 0θπ

, OA a ="""#"#, OC c ="""## , t OE tc ="""##

(1) t cos θ

AE tc a =?"""##"#, DB c =+"""###, a c ?="## cos θ

, AE DB ?="""#"""#

()()

cos 1cos t θθ+=

+

(2) E OC θ , OC O, C , cos

r θ= E OC , 0 t 1 11r ?<< ,

cos θ r (r + ) ,

0 t 1

0 ( )1r + (r + )

r , θ ,

π

θπ

(3) 1cos 8θ=? AE BD F , BEF

, t =, OF =

"""#

, F AE 1: ,

OABC , BEF

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