2010年中考数学压轴题100题精选(81-90题)答案

2010年中考数学压轴题100题精选（81-90题）答案

9

，c＝－3． ···································································· 3分 439

（2）由（1），得y＝x2－x－3，它与x轴交于A，B两点，得B（4，0）．

44

∴OB＝4，又∵OC＝3，∴BC＝5． 由题意，得△BHP∽△BOC， ∵OC∶OB∶BC＝3∶4∶5，

∴HP∶HB∶BP＝3∶4∶5，

∵PB＝5t，∴HB＝4t，HP＝3t．

∴OH＝OB－HB＝4－4t．

3

由y＝x－3与x轴交于点Q，得Q（4t，0）．

4t

∴OQ＝4t． ······································································································· 4分 ①当H在Q、B之间时， QH＝OH－OQ

＝（4－4t）－4t＝4－8t． ········································································ 5分 ②当H在O、Q之间时， QH＝OQ－OH

＝4t－（4－4t）＝8t－4． ········································································ 6分 综合①，②得QH＝｜4－8t｜； ········································································ 6分 （3）存在t的值，使以P、H、Q为顶点的三角形与△COQ相似． ······················· 7分

①当H在Q、B之间时，QH＝4－8t，

4 8t3t

若△QHP∽△COQ，则QH∶CO＝HP∶OQ，得＝，

34t

7∴t＝． ········································································································ 7分

32

3t4 8t

若△PHQ∽△COQ，则PH∶CO＝HQ∶OQ，得＝，

4t3

即t2＋2t－1＝0．

∴t1

1，t2

1（舍去）． ······················································· 8分 ②当H在O、Q之间时，QH＝8t－4．

8t 43t

若△QHP∽△COQ，则QH∶CO＝HP∶OQ，得＝，

34t

25∴t＝． ········································································································ 9分

32

3t8t 4

若△PHQ∽△COQ，则PH∶CO＝HQ∶OQ，得＝，

4t3

即t2－2t＋1＝0． ∴t1＝t2＝1（舍去）． ···················································································· 10分

725

综上所述，存在t的值，t1

1，t2＝，t3＝． ··························· 10分

3232

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