Sueh
P濴ȾPBαߤ򤫤ȡ߼B, C, Aʱ߼ѤεդŬ˻Ƴˡ
ȾľPD, PEȤθ򤽤줾D', E'ȤТPD'B, PCE'ϤȤѷ
D'BD=D'BP-DBP=60-DBP=BPC-BAC-DBP=PCEʤɤ颤D'BDᢤPCE
Ⱦ=PD'=+=, DB=ECʤɤȤ狼롣
٤ˤAD*DB=D'D*DC=*, AE*EC=E'E*EB=*
äAD:AE=*/DB:*/EC=(3*5):(1*7)=15:7, AE=7/3cm

ʤѤǤ꤫Ȼפޤ
127ڡ 1:07:24 46815
baLLjugglermoka
BDPȢPECBDEC碌ѷˤʤΤǡѤDP:PC=1:4,BP:PE=4:3
BAEBPDꡢȤη׻
127ڡ 2:56:17 46816
ˤ
P濴αߤȤޤɤǤ⤤ɡǤ(T_T)
Ķļˡ 127ڡ 3:49:26 46817
Ȥ
ɸP(0,0),B(-sqrt(3)*a,-a),C(sqrt(3)*a,-a)
Ȥȱ߼ѤP濴Ȥ
Ⱦ2*aα:x^2+y^2=4*a^2ˤΤA(b,sqrt(4*a^2-b^2))
ľAB:y=(sqrt(4*a^2-b^2)+a)*(x+sqrt(3)*a)/(b+sqrt(3)*a)-a
ľCD:y=-sqrt(3)*x/3
ľAC:y=-(sqrt(4*a^2-b^2)+a)*(x-sqrt(3)*a)/(sqrt(3)*a-b)-a
ľBE:y=sqrt(3)*x/3
ľAB,CDθD,ľAC,BEθE5cmξ2Ǥ
XMaxima

part(solve([y=-sqrt(3)*x/3,y=(sqrt(4*a^2-b^2)+a)*(x+sqrt(3)*a)/(b+sqrt(3)*a)-a],[x,y]),1)$
part(solve([y=sqrt(3)*x/3,y=-(sqrt(4*a^2-b^2)+a)*(x-sqrt(3)*a)/(sqrt(3)*a-b)-a],[x,y]),1)$
num(factor((b-rhs(part(%o1,1)))^2+(sqrt(4*a^2-b^2)-rhs(part(%o1,2)))^2-25))$
part(factor(-expand((part(%,1)+part(%,2)+part(%,3))^2-(%-(part(%,1)+part(%,2)+part(%,3)))^2)),2)$
factor(rhs(part(%o2,1))^2+rhs(part(%o2,2))^2-9*(rhs(part(%o1,1))^2+rhs(part(%o1,2))^2))$
part(-num(%),3)$
part(factor(-expand((part(%,1)+part(%,2))^2-(%-(part(%,1)+part(%,2)))^2)),2)$
%th(4);%th(2);

16*a^2*b^4-100*sqrt(3)*a*b^3-96*a^4*b^2+200*a^2*b^2+625*b^2+400*sqrt(3)*a^3*b+144*a^6-1200*a^4(1)
91*b^2-160*sqrt(3)*a*b+192*a^2(2)

μbˤĤƲ򤤤b=8*sqrt(3)*a/13,b=8*sqrt(3)*a/7
μ
1200*a^2*(9*a^2-52)*(147*a^2-325)/28561,1200*a^2*(3*a^2-28)*(9*a^2-175)/2401
μa=-5*sqrt(13)/(7*sqrt(3)),a=5*sqrt(13)/(7*sqrt(3)),a=-2*sqrt(13)/3,a=2*sqrt(13)/3,a=0
μa=-5*sqrt(7)/3,a=5*sqrt(7)/3,a= -2*sqrt(7)/sqrt(3),a=2*sqrt(7)/sqrt(3),a=0
бbμ(1),(2)٤Ƥβ򤬤ǤΤaĹʤΤ
(a,b)=
(5*sqrt(13)/(7*sqrt(3)),40*sqrt(13)/91)(3)
(2*sqrt(13)/3,16*sqrt(39)/39)(4)
(5*sqrt(7)/3,40*sqrt(21)/21)(5)
(2*sqrt(21)/3,16*sqrt(7)/7)(6)
(3),(5)
2*a*b^2*sqrt(4*a^2-b^2)+4*sqrt(3)*a^2*b*sqrt(4*a^2-b^2)-12*a^3*sqrt(4*a^2-b^2)+2*sqrt(3)*a*b^3-4*a^2*b^2-25*b^2-8*sqrt(3)*a^3*b+24*a^4
Բ
(6)Dxɸsqrt(7)/2Բ,((5)xɸ5*sqrt(21)/12ǤԲ)
(4)sqrt((sqrt(39)/2-16/sqrt(39))^2+(sqrt(13)/2-44/(3*sqrt(13)))^2)=sqrt(49/9)=7/3()
˭ԡ 127ڡ 5:34:21 46818
ǯ
ǽϡޤǵơ7/3
ͤľơ
ѤδطꡢAEBPDB(1)
ADCPEC(2)
PD=PQȤʤQPE˼СPDBPQCǤ롣
ޤAEB=PDB=PQCꡢQEC=EQCȤʤꡢ
ΤˡEQCջѷȤʤΤǡDB=QC=ECǤꡢ(3)
CQE˿CR򲼤QR=ER¨Q,RPE3ʬˤʤ롣
PRC=90롢RPC=60ꡢPCRѷȾʬ
顢PC:PR=4:2뤤ϡPC:PE=4:3(4)
(2)(4)ꡢPE:PC=:=5:ACAC=AE+EC=20/3(5)
(1)ꡢBP:PD=:=AB:AE=5+DB:AE=5+EC:AEʤΤǡ5+EC=4*AE(6)
ȤϤŪ(5)(6)ꡢ5*AE=5+20/3=35/3ΤˡAE=7/3
PE:PCϿưפǤºݤ˵ȤǶϫޤ#46816baLLjugglermokaΤϤޤǤ
ɵ(6)ʲ򼡤Τ褦˲򤱤ϢΩɬפʤä
ABCѤǡBDC=CEBʤΤǡABդȹͤι⤵ACդȤι⤵ͤȡϡDC:BE=: (6)
顢AB=AC*/=(20/3)*(7/5)äơAB=5+BD=28/3BD=13/3
(5)ꡢAE=20/3-13/3=7/3

128ʶ 17:32:15 46819
Sueh
ʤۤɡ #46816 ͡ #46819 ͤβ򸫤ٶˤʤޤ
ޤȤȡ
PBDȢPCE碌ѷˤƱ򼨤Ƥ顢
AB+AE=AD+AC =AD+AD*4/3 (袤CAD梤CPE)
AB:AE=PB:PD (袤BAE梤BPD) =4:1
Ȥȳڤ˵ΤǤ͡

A, D, P, EޤǤϵŤƤΤ٤ͤƤޤǤ
ʾ嵭CAD梤CPECA/CP=CD/CEˤܤǤ"=AD/PE"ȤޤǤ
BAE梤BPDˡ
127ڡ 11:27:18 46820
ޥ
¤ϡ552λȤ󤷤Ǥm(__)m
MacBook Pro 127ڡ 13:10:34 HomePage:46821
Ȥ
552긫ޤǼĤɤȤ
ʬβˡƤʤäΤǤäƤߤޤ

ɸP(0,0),B(-2*a,0),C(a,-sqrt(3)*a),R(b,0)Ȥ
ľCR:y=sqrt(3)*a*(x-b)/(b-a)
3y=6/bxͤФ
Ax^2+y^2=4*a^2ˤ뤳ȤѤ1/8
(b+2*a)*(6/b+sqrt(3)*a)/2-8*a*6/bȤ
2ǤƤx=6*a/bȤ3ϢΩXMaxima Ǥ

rhs(part(solve(6/b=sqrt(3)*a*(x-b)/(b-a),x),1))$
num(factor(%^2+(6/b)^2-4*a^2))$
num(factor((b+2*a)*(6/b+sqrt(3)*a)/2-8*a*6/b))$
part(part(solve([%o2,%o3,x=6*a/b],[a,b,x]),2),3);x=7/2()
˭ԡ 128ʶ 3:04:21 46822
ֿء׾ι
xserver 󥿥롢Ȥꤢǯ֤ʡءˡ
ȤäƤߤΤǡʴ򤷤˸ƤƤ͡
ޤ򥢥åפޤ!!ɥᥤ̾ϡ֥ʼž֡ˡס֥եå󥰡ˡסmathʿءˡפͻ礫Ƥޤ

http://chafima.org/sansu/s1040/sansu1040r.html

ͥ饦ˤꡢx/y*4/1*y/(y+5)=1, 5/y*4/3*y/(x+y)=1 ǡ
ϢΩ򤭤ޤ

128ʶ 15:32:58 46823
ˤ⡼
Фˤ
Ǥ
٤ǥ档ٲ˼档
ĴΤDz򤤤Ƥߤϫޤ
PECȢPDB碌ѷˤΤ˵ŤΤ˻֤ä


PECȢPDBECDBǹ碌ѷˤ롣
DP+PE=ܭ᭤顢PC=PB=


BPD梤BAEBP:PD=4:1顢AE=XȤ AB=4X DB=4X-5
DB=EC=4X-5 AC=X+4X-5=5X-5


CEPCDAPE:PC=4:3顡AC:AD=4:3=5X-5:5
X=35/15=7/3

ʾ

#46767 ǿ줿̳ξʻɮ̲ᡣ
ȤǯŻǼܡ
̸ǭ 128ʶ 19:24:41 46824
N
ܱߤȥ٥ڤǡ̲­ǤޤƬ㤨Ƥޤ
1210 0:10:45 46825
cocogoo
;ȤϤDz򤭤ޤ
1210 1:36:25 46826
٥륯åĥ
νäȤơ
УŤĹѷƣУäȣ£УĤȣãƣŤˤʤäƣУšţơ31ȣģСУá14£СУš43ˤʤꡢ٥ڤǣġģС1513šţá713£УĤȣãƣŤģ¡ţäʤΤǡġ5׻ƣš7/3ˤʤޤ
1210 2:41:30 46827
ǯ
#46825, #46827. ֥٥ڤפդϻϤΤޤ
ڤ٥ĤΥ֥ϢۤȤȤȤ⡣
䤬عκϡ٥ĤʤƸȤʤǤ󡥡
1210 20:28:13 46828
٥륯åĥ
ΤޤǤˤǤθդ򸫤ơʤΤǻȤäƤߤޤ٥ڤ
1210 21:41:44 46829
KKK
٥ڤäͳرǽäʤ
͡ 1213ʿ 15:20:09 46830
ֿء׾ι
֥٥ڤפ֤ȰƤΤǤ͡ΤޤǤ͡ߥ󥰤Ǥ͡
ѷʬĹδطüŪˤΤ˺ŬǤ͡줫ȤȻפޤ
1213ʿ 16:19:44 46831
ޥ
ȡ12/22ʶˤ˷ˤơϡʥѥϤοͤ⤤ޤˤ˺ǯޤʤꡢ롼Ǥ19:00Ϥǡ֤󤺡äƱŹˤޤ̣ϡ

masaru-y@sansu.org

ޤǡϢޤm(__)m
MacBook Pro 1213ʿ 22:55:05 HomePage:46832
鯤ο
A,D,P,EƱ߼ˤ뤫顢
αߤϡADPAPE̤γܱߤǤ롣
顢ADPAPEΡ줾ˤ
ϢǤƤޤ
DAPPAE¤Ȥȡ
DP:PE=1:3ϡsinsin¡1:3
Ǥ롣
ܦ¡60ȡsinβˡ
ϢΩȡ
sin3/213
cos7/213
sin¡33/213
cos¡5/213

ޤAPE=BAP+PBA2
ƱͤˤơAPD2

AE=xȤȡ
ADAEsin2¡sin25:x
x=5*(sin2/sin2)

2ܳѤθơx=7/3
//

1213ʿ 23:15:22 46833