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=180-(90-EAF)=90+EAF=90+PEF,K=12EPF=12(180-2PEF)=90-PEF,,EQF+K=180.KFQE.PK=PE=PF,P.,PQ=PF.,PQF=PFQ=PFB=FAB=FAH.AHQF.,PHA=QHA=180-QFA=90,,PHAB,PQAB.CPQ.CPAB.(1)a2+(y1+y2)a+y1y2=0,(a+y1)(a+y2)=0.y1=-ay2=-a.(2)a0,f(x),AB-a0,,x;a0,f(x),AB-a0,,x.f(x)x.(3)ax2+bx+c0{x|xmxn}(nm0),,a0,b0,c0.,cx2+bx+a=0x1=1m,x2=1n.,cx2-bx+a=0x1=-1m,x2=-1n.nm0,,-1n-1m.cx2-bx+a0x-1mx-1n.(,246004,246142)(5)(7,42)1.x2-3x+1=0x4-px2+q=0,(p+q)2008().(A)2(B)4(C)6(D)82.y=1x2+ax+b(,ab)().(A)a2-4b0(B)a2-4b0(C)a2-4b0(D)ab,3.ABCr,BC=a,AC=b,AB=c,hahbhc,ha+hb+hc=9r.ABC().(A)(B)(C)(D)4.xyz,x(y-z)=y(z-x)q=z(y-x)q2,q().7120071(A)-152(B)152(C)-1+52(D)1-525.12,,().(A)1(B)6(C)4(D)6.1,ABC,AB1C,I.:IACBI;ICBAI;IBACI.l1l2l3,().(A)l1(B)l2(C)l3(D)(7,28)1.2006(x-y)+2007(y-z)+2008(z-x)=0,20062(x-y)+20072(y-z)+20082(z-x)=2008.z-y.22.2,ABCD,AB=10,BC=17,CD=13,DA=20,AC=21.BD=.3.xyz(,xyz),,.,.34.3,RtABC(C=90)P,AP=AC=a,BP=CP=b(ab).a2+b2a2-b2=.(20)ab(ab),a+b=m+2,ab=4m..4(25)4,OABCABACPQ,ABCT.PQI.:ITBTC.(25)x31+x32++x38-x391,,x1,x2,,x92001,2002,,2009,8x9x1+x2++x8.x9.1.C.x2-3x+1=0,4-p2+q=0,4-p2+q=0.=(-3)2-4=50,,22.p=4-42-2=2+2,q=22(2-2)2-2=22.+=3,=1,,2+2=(+)2-2=7,22=()2=1.,p=7,q=1.,(p+q)2008=82008=(84)502=4096502.2.C.y=1x2+ax+b=44x+a22+4b-a2.(1)a2-4b0,x2+ax+b=0,,y;81(2)a2-4b0,0y44b-a2.,a2-4b0,y=44b-a2.3.B.SABC=12aha=12bhb=12chc,ha+hb+hc=2SABC1a+1b+1c.SABC=12r(a+b+c),ha+hb+hc=9r,(a+b+c)1a+1b+1c=9,a(b-c)2+b(c-a)2+c(a-b)2=0,,(a-b)2=(b-c)2=(c-a)2=0.a=b=c.4.B.q1.x(y-z)+y(z-x)1+q=z(y-x)q2.x(y-z)+y(z-x)=z(y-x),,1+q=q2,q2-q-1=0.q=152.5.C.a=12,c,c2-b2=a2=144.144=2432,,(c+b)(c-b)=722;(c+b)(c-b)=364;(c+b)(c-b)=188;(c+b)(c-b)=169;(c+b)(c-b)=483;(c+b)(c-b)=246.c+bc-b,:a=12,b=5,c=13;a=12,b=9,c=15;a=12,b=16,c=20;a=12,b=35,c=37.6.C.ABC,abc.AI=x,BI=y,CI=z(xyz),,l1=x+b+a+y=(b+y)+(a+x);l2=z+a+c+x=(a+x)+(c+z);l3=y+c+b+z=(b+y)+(c+z).55,CAD,CD=a,ID.,ICDICB.AD=a-b,ID=y.AID,AI+ADID,x+(a-b)y.,b+ya+x.,c+zb+y.,c+zb+ya+x.l1l2l3,l3.1.2008.z-y=t.z-2x+y=0.,z-x=t2,,x-y=t2.t=z-y=2008.2.105.66,BEACE,DFACF,BGACDFG,BEFG,BDGABECDF.ABC,p=12(AB+BC+CA)=24.BE=22124(24-10)(24-17)(24-21)=8.,ADC,DF=12.DG=DF+FG=DF+BE=20.AE=AB2-BE2=6,CF=CD2-DF2=5,BG=EF=AC-AE-CF=10.,BD=DG2+BG2=105.3.495.xyzabc(abc),cba.91200711a9,1b9,1c9,abc-cba=(100a+10b+c)-(100c+10b+a)=99(a-c)99,xyz99.998:198,297,396,495,594,693,792,891.,495.4.3.,BPCCAP.77,BPACK,PC=PK=b,BK=2b.PCKACP,CK=b2a.BK2=BC2+CK2,(2b)2=a2+b2a2,,a4+b4=4a2b2.,(a2+b2)2=6a2b2,(a2-b2)2=2a2b2(ab).a2+b2a2-b22=3,a2+b2a2-b2=3.ab,,m.,abxx2-(m+2)x+4m=0.,=(m+2)2-16m=m2-12m+4.m2-12m+4=k2(k),m2-12m+4-k2=0.m,=(-12)2-4(4-k2)=4(32+k2).,32+k2.32+k2=(k+n)2(n).32=(k+n)2-k2=n(2k+n).,n2k+n.32=132=216=48,,:(1)n(2k+n)=132=1(2k+1),k;(2)n(2k+n)=216=2(2k+2),k=7,m=15,5,12,13;(3)n(2k+n)=48=4(2k+4),k=2,m=12,6,8,10.,5,12,136,8,10.88,OA.,OABAC,OAPQ.,OIA.OPOTAT,OP2=OIOA=OT2.,OTIOAT.OTI=OAT.TST,STC=CAT.OTST,OTS=OTI+ITC+CTS=90.CTI=90-(OTI+CTS)=90-(OAT+CAT)=90-CAO=90-12A.,BTI=90-12A=CTI.,ITBTC.x1,x2,,x92001,2002,,2009,2001,2002,,20091,2,3,4,5,6,7,8,931,8,7,4,5,6,3,2,9,,x31+x32++x395.x31+x32++x28-x39=x31+x32++x38+x39-2x39.x39a9.x31+x32++x39:(1)5-2a90,5-2a9;(2)5-2a90,15-2a9.,5-2a9=115-2a9=1.,a9=2a9=7,x9=2008x9=2003.8x9x1+x2++x8,,x9=2008.(,277200)02