P(甲获胜)

63105 ，P(乙获胜) ． ····································································· （7分） 168168

35

， 88

····································································································· （8分） 这个游戏不公平． ·

23．（本题满分8分）

解：（1）证明：过点A作AE⊥BC，交BC于点E． AB AC， AE平分BC．

······································ （2分） 点O在AE上． ·

又 AP∥BC， AE⊥AP．

AP为⊙O的切线． ································ （4分） （2） BE

P

1

BC 4，

2

（第23题答案图）

OE 3．

又 AOP BOE， △OBE∽△OPA． ··································································································· （6分）

43BEOE

． ． 即

AP5APOA

20

AP ． ················································································································· （8分）

3

24．（本题满分10分） 解：（1）过点A作AF⊥x轴，垂足为点F，过点B作BE⊥x轴，垂足为点E，

则AF 2，OF 1．

OA⊥OB，

AOF BOE 90°． 又 BOE OBE 90°， AOF OBE．

Rt△AFO∽Rt△OEB．

BEOEOB

2． OFAFOA BE 2，OE 4．

B(4，2)． ····················································································································· （2分） ，2)，B(4，2)，O(0，0)的抛物线为y ax bx c． （2）设过点A( 1

2

1

a ， 2 a b c 2，

3

16a 4b c 2，解之，得 b ，

2 c 0.

c 0．