2021-2022学年湖南省长沙市岳麓区九年级（上）第三次月考数学试卷（附答案详解）

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2021-2022
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17BC=2CD,4BCD=90°B=60°•••Z.ACB=105°Z.ACD=Z.ACB-BCD=45°Rt#1$AD=CD".AC=yjAD2+CD2=y/2CDBC2CD——=—--V2ACy/2CD.•.ABC᠗.2(3)•••ABC᠗$BC᠗$4B᠗BC=y/2AB•••ABC"$483H$ᓽ&4cB90°AABC=90஺ᡈ4BAC=90°জ&4BC=90஺$=8BE1xE,=CCF1EB=CCG1xG,᝞3,•••Z.AEB="=LABC=90°•••BCF+Z.CBF=^ABE+CBF=90"/.BCF=/.ABE:BCFs&ABEBFCFBC—=—=—=v2AEBEAB.?IE=a,ᑣB/7=y/2AE=\[2av4(3,0)OE=OA+AE=3+Q8Ḅᙶ᪗$ᓽBE=CF=V2BE=2,CG=EF=BE+BF=+V2a,8(3+a,V2)•OG=OE-GE=OE—CF=3+Q—2=1+Q•C(14-a,V24-V2a)•3ஹ஺ᙠᙠᦪy=5(g>0)Ḅ$•V2(3+Q)=(1+a)(V2+V2a)=kA%=-2(67)$a=12:.k=4A/2ঝ2B4C=90஺ஹ=CCMlx=3BNlxN,᝞4,M18⚓$ᐳ21⚓

18Z.CMA=Z.ANB=LBAC=90°•4MCA+^MAC=MAC+NAB=90°Z.MCA=NABMCAs^NAB•••BC=;AB,2AB2=BC2=AB2+AC2•••AC=AB•••AMCA^^NAB(AAS)AM=BN=V2OM=OA-AM=3-^/2.CM=4N=b,ᑣON=04+AN=3+b,C(3V2,fa),B(3+b,V2)•.•BஹCᙠᙠᦪy=g(x>0)Ḅ$•••(3—\[i)b=V2(3+b)=kA6=9ᡈ+12k=18+15V2qᡠ»$kḄh4eᡈ18415V2(1)ᵫ3½_¾¿ᩩḄi$ᦑ◤ᑖ3ÂÃÄÅÆ.ÇÂÃÄ1$3½_iᡃḄᔲ᠗$ᦑ◤⌕ᑖËÅÆ.(2)=CABḄᚖ>CD,᪀⌼ÏÐᨵᱯÒḄ"$ᓽᵨCDÓᔜᐵÕ⊤×ᩭ$᧕DBCEACaG.(3)ᵫ⚪5HsBC=/Z4B,SjAABC"$AB3H$ᓽÛᑖ&48c=90஺ᡈNa4c=90஺ÏÂÃÄÅÆ.ÝÞ>᪀⌼ᚖ"ßà$A
ᡈᐰy$âᑭᵨãḄᐵÕÓBஹCḄᙶ᪗⊤×ᩭ$âäᐭy=⊤ᓝç.⚪ὃlmè_éḄᳮnêᵨ$"$
nᐰyḄᑨ_nឋL$ëìíᦪḄឋL$ᑖËÅÆîï.⚪ᐵᳮè_éðêᵨᐸឋLòᓄᩩG$ᙠ"ᙶ᪗Õ1Óôs"᪀⌼ᙠᚖ"ßàõö÷øù.25.ூᫀ௃(1)••,2úᦪy=ax2+bx+4(a*0)Ḅü=4(4,0),6(1,0),.(a(4)2+b,(4)+4=0la4b+4=0

19AE=-J,•.þ2úᦪḄ⊤ÿ
y=-x2-3%+4(2)᝞8y••PD஻y•DPB=/-OEB,•DPB=2(BCO,•OEB=2/-BC0,•ECB=EBC,•BE=CE,0E=a,ᑣCE=4—Q,:.BE=4—a,ᙠRtZkBOEᵫᳮBE2=0E2+0B2,:.(4-a)2=a2+I2,a=8••E(O,QBEᡠᙠ⊤
y=fcx4-e(fcH0),fk-04-e=—**.s8,l/c-14-e=0ffc=--is8,le=T•••BPḄ⊤
y=-^-x+~88(3ᨵᨬᜧ%.QB᝞IPDJACK*LஹN,&B'yḄ()AC*M,AC⊤
y=mx+n,•4(-4,0),C(0,4),cm,AC⊤
y=%4-4,MḄᙶ᪗
(1,5),:.BM=5,vBM“PN,PNQs&BMQ,-20⚓ᐳ21⚓

20P(@o,45—3ao+4)(-4