2019平谷一模数学试题及答案

24．（1）证明：∵AC切⊙O于点A，

∴∠BAC=90°． ········································································· 1 连接AD．

∵点E是BD的中点，

CDE∴∠BAE=∠DAE． F∵AB是⊙O的直径， ∴∠ADB=90°． BAO∵∠CAD+∠DAB=∠DAB+∠B=90°， ∴∠CAD=∠B．

∵∠CAD+∠DAE =∠B+∠BAE， ∴∠CAF=∠CFA． ···································································· 2 ∴AC=CF． ············································································· 3

（2）解：∵AB=4，AC=3，

∴BC=5． ················································································ 4 ∵AC=CF=3， ∴BF=2．

∵cosB?∴BD=

BDAB4??， ABBC516． ············································································· 5 5126∴AD=，DF=．

551∴tan∠BAE= tan∠DAE = ························································· 6

225．（1）3.0； ····························································································· 1

（2）如图； ··························································································· 3

（3）1.2或1.6或3.0． ············································································· 6

26．（1）m； ······························································································· 1

（2）∵y?x2?2mx?m2?3??x?m??3，

∴抛物线顶点坐标为（m,－3）． ························································ 2

∵抛物线经过点A，B时，且AB∥x轴， ∴抛物线对称轴为x=m=2． ······························································· 3

∴抛物线的表达式为y?x?4x?1； ················································· 4 （3）0?m?1． ···················································································· 6

2227．（1）∠BCD=120°－α． ············································································· 1 （2）解：

方法一：延长BA使AE=BC，连接DE． ······ 2

D 由（1）知△ADC是等边三角形，

∴AD=CD．

∵∠DAB+∠DCB=∠DAB+∠DAE=180°， ∴∠DAB=∠DAE．

C∴△ADE≌△CDB． ···················· 3

P∴BD=BE．

∴BD=AB+BC． ·························· 4

BEA方法二：延长AB使AF=BC，连接CF． ······ 2

∠BDC=∠ADE． ∵∠ABC=120°，

D∴∠CBF=60°．

∴△BCF是等边三角形． ∴BC=CF．

∵∠DCA=∠BCF=60°，

∴∠DCA+∠ACB=∠BCF+∠ACB． CP即∠DCB=∠ACF． ∵CA=CD，

BAF∴△ACF≌△DCB．····················· 3

∴BD=AF．

∴BD=AB+BC． ·························· 4 （3）AC，BD的数量关系是：AC?3BD； ········································· 5 2位置关系是：AC⊥BD于点P． ······································· 6

28．（1）22； ·························································································· 1

（2）22?r?4； ················································································ 3 （3）?25?2?t??5?2或6