ޥ
Υˤꡢޤ٤Ƥޤޤޤ

ܴۤλԷǼĤΥѥɥեԽ褦viޥɤưȤ˥饤ȤΥߥʥ뤫ϤȤ⤹ȤʤʤäƤޤޤpingǤäƤʬꡢ֤㤢ʡפȤʬäΤǤ˥ޥ󤬤櫓ǤϤʤΤǡФδҤΥ֡ȤԤĤʤȤˤʤäƤޤޤƤ褦䤯ۤɥ֡ȤλȤ櫓Ǥ

ܤϤ줫ʤȤϤäƤֽʤΤǺϤ⤦ʤƤϤʤޤ...ε٤߻֤ˤ뤳ȤˤޤĴ뤳ȤˤʤޤȤˤ¿γͤˤǤ򤪤ƤޤޤޤǤm(__)m
PowerBook G4 818ڡ 1:04:47 MAIL:masaru-y@sansu.org HomePage:25625
ڼ
ʤʤǤʤơۤޤ
Ż˺٤ʤ٤ˤФäƤ
͡ 818ڡ 1:23:38 MAIL:iida@ae.keio.ac.jp 25626
tomh
᤺˥ɤƤޤ (^^;
ȤꤢҤäƤۤäȤޤ͡
ԡ 818ڡ 1:28:10 MAIL:tomh@yahoo.co.jp HomePage:H to M25627

ϻѷηˤʤǤ̤͡ǤƤƤءäȻפä

ɤʡ
̤̪ 818ڡ 1:39:00 MAIL:ishizaki@qa.so-net.ne.jp 25628
ȥȥ
öƿɡܤƤޤФƤޤ
ϹֽʤΤǤ⤦ޤ
ѷηˤʤȤ˷ǤäƿޤƤߤޤ
ʼ˸лԡ 818ڡ 1:47:35 MAIL:h-sakai@zb3.so-net.ne.jp 25629
ڼ
ܣϣФԳѤξ߳Ѥξǡ򤬣̤ꤢΤǤϡ
裲βϻǤϵޤޤ
͡ 818ڡ 1:59:06 MAIL:iida@ae.keio.ac.jp 25630
Gou
Ȥꤢܣϣ¤ľѤȤƲ򤭤Ϥޤ
ۥȤˢϣ¤ηˤʤǤ͡
Τؤ󡢺٤Ȥʺ˹ͤޤ
䥹ߥʥ(v_v)Zzz..
TAHICHI?! 818ڡ 3:01:21 25631
ʤ
OAP>90ξ
λѷ٤Ǥޤ
http://www3.sansu.org/tables/san08181207.GIF
̳ƻ 818ڡ 4:01:31 MAIL:naka@sansu.org HomePage:naka's Home Page25632
ʤ
OAP<90ξ
MN=(12/7)*37 Ȥʤ褦Ǥ
̳ƻ 818ڡ 4:14:20 MAIL:naka@sansu.org HomePage:naka's Home Page25633
CRYING DOLPHIN
ޤ򤷤Ƥ뤦ˡͤǤлѷη
̵뤷ƹʤȤƤդΤǡѷ٤
ʣϣ£ľˤʤ褦ˤˤȤ˽ˡ
ȡƤľѻѷȯǤƽλ
ǯԥ奦ȡ 818ڡ 8:57:33 HomePage:θ³äƤɤΤ餤25634
ʤƱǤ
(#25632 http://www3.sansu.org/tables/san08181207.GIF)
򤪼ڤꤷޤ
OAB梤ONMڤ
POA梤QOB(ž)
NOA梤MOB(N,M줾)
NOAMOB,ON:OM=OA:OB
BOAMON(NOB),ON:OM=OA:OB
袤OAB梤ONM
Ȥޤ
818ڡ 9:02:42 25635

ϣ¢梤ϣΣͤͭ̾ϣΤϣλѷĤǣȤ狼롣
818ڡ 9:45:51 25636
kasama
Ϥ褦ޤ
Ĥ̤ꡢãĤdzھȻפ䡢17.14285714򤦤ޤͭǤɡؤǥޥ()ĥĤȤޤ(v_v;)ɤä(-o-;)
818ڡ 10:41:26 25637

ɸǹͤƤʤȤ
ɸΣ'򣳡λѷ顢ϣαĹߤ
(-25,0)(-18,0)(0,24)(-9,12)
ϡǤդǤΤǡ礨ŢOAB90٤Ȥơ
(-18,6)ϡϣФεΥơʢ252+242=1201)
ȡϣ¤Ȥꡢơ(-144/7,318/7)
ȣꡢɸơ(-135/7,180/7)
֤ͣεΥơ120/7

ϡ2̤ꤢꤽǤ͡OAPԳѡ߳Ѥȡ

ƽ 818ڡ 11:05:50 HomePage:θ줳ߤ󡪡25638
ޥ
OAP߳Ѥξ곰Ǥʸ줵ĺޤŦ꤬ȤޤڼԤ󡢤ʤ󡢷

ˤꤴǤ򤪤...Ȥ⤤ä㤤ޤǤ礦ʤޤ¿ϱԳѤξ礫ͤȤϻפΤǤ...
PowerBook G4 818ڡ 10:47:32 MAIL:masaru-y@sansu.org HomePage:25639
uchinyan
Ϥˤϡϼꤳޤ (^^;
ɤϡ¿ʬƱǡOAB ONM ƳON = 20 Фޤ
¤ϡǽ顢̤ˡϺƤΤǤ
ͥνȡ 818ڡ 11:15:17 MAIL:uchi@sco.bekkoame.ne.jp 25640
Ȥ
ͤɸˤʣǺɸȤڤäǤ
褺դοޤO(0,0),A(7,0)Ȥ
ǾOA=7,OAP=84
Pyɸ24P(s,24)
ǾAP=30ˤɸ
AP=SQRT((s-7)^2+24^2)=30
solve((s-7)^2+24^2=900,s);s=25,s=-11(ޤԲ)
ȭȤP(25,24)
OP=SQRT(1201)'
OAB梤OPQOA:OP=7:SQRT(1201)=AB(=6):PQ''
衡PQ=6*SQRT(1201)/7
ޤAB=6A(7,0)B(a,b)Ȥ
AB=SQRT((a-7)^2+b^2)=6
solve((a-7)^2+b^2=36,b);b=SQRT(-a^2+14*a-13)
B(a,SQRT(-a^2+14*a-13))
ǢOAB梤OPQ
O濴ˢOABžȢOPQ
POA=QOB
γ٤ϭ,'Ȥ
sinPOA=24/SQRT(1201)
cosPOA=25/SQRT(1201)
Z˳ѦȤž
濴rܤr*(cos+%i*sin)*Z
Ǥ뤳ȤȤB˲ž
Qˤ뤳Ȥˤ뭤
B=a+%i*SQRT(-a^2+14*a-13)
ޤ''r=SQRT(1201)/7˭,Ȥ
expand((SQRT(1201)/7)*(25/SQRT(1201)+%i*(24/SQRT(1201)))*(a+%i*SQRT(-a^2+14*a-13)));
Q=%i*(25*SQRT(-a^2+14*a-13)+24*a)/7-(24*SQRT(-a^2+14*a-13)-25*a)/7
̤κɸľ
Q=(-(24*SQRT(-a^2+14*a-13)-25*a)/7,(25*SQRT(-a^2+14*a-13)+24*a)/7)
ȭM
M=( (a-(24*SQRT(-a^2+14*a-13)-25*a)/7)/2,(SQRT(-a^2+14*a-13)+(25*SQRT(-a^2+14*a-13)+24*a)/7)/2 )
N=((7+25)/2,(24)/2)=(16,12)εΥ
(%i1) EXPAND(((a-(24*SQRT(-a^2+14*a-13)-25*a)/7)/2-16)^2+((SQRT(-a^2+14*a-13)+(25*SQRT(-a^2+14*a-13)+24*a)/7)/2-12)^2);
(%o1) 14400/49
(%i2) sqrt(%);
(%o2) 120/7()
ϼʬĤʤʤ󤸤ʤȻפޤ
(ˡ̵뤷ƤΤ)ʤƥۥåȤޤǤϡ
˭ԡ 818ڡ 15:20:33 MAIL:fttnm528@ybb.ne.jp 25641
uchinyan
äȡǼɤߤޤĤʤ顢ʤοޤ٤ƤǤ͡
ޥ뤵
#25639
OAP߳Ѥξ곰Ǥ
ʸ
䤿ܣϣФϣ̤ǤΤȤޤ
䤪䡣OAP < 90 ǤϤޤޤ򤱤ޤ ^^;
OAP > 90١δְ㤤ϡOAP ǤϤʤ AOP δְ㤤Ǥϡ

ĿŪˤϡžߤȡĤĤʣǿȤʤ밭ʤޤ (^^;
嵭βޤơͤޤǤ˼ޤ޷ռʤСȴñǤ
ޤO(0), A(a), B(b)a ϼ¿ǡa > 0Ȥޤ
ޤβž̾ɽʣǿ z ȤޤȡP(za), Q(zb) ǤʤߤˡAOP = arg(z) (= z г)Ǥ
˾򼰤ˤƤޤʲǤϡRe(z), Im(z) ǡz μz~ z ʣǶɽޤ
βžѤ 0 180٤Ȥư򼺤ʤΤǡIm(z) >= 0 ȤƤޤ
OA = |a| = 7, AB = |a - b| = 6, AP = |a * (z - 1)| = |a| * |z - 1| = 30
OAP = 1/2 * OA * |P ε| = 1/2 * |a| * |Im(za)| = 1/2 * |a|^2 * |Im(z)| = 84
N = 1/2 * (A + P) = (a(z+1)/2), M = 1/2 * (B + Q) = (b(z+1)/2)
Τϡ
MN = NM = |a(z+1)/2 - b(z+1)/2| = 1/2 * |a - b| * |z + 1|
ޤñˤޤ
|a| = 7, |a - b| = 6, |z - 1| = 30/7, |Im(z)| = 24/7
ǸĤ顢z ϡ1 Υ 30/7 ˤ 24/7 οʬޤ
ޤȡ줫顢|Re(z) - 1||Im(z)||z - 1| = 345 ľѻѷǤ뤳Ȥʬޤ
ǡ|Re(z) - 1| = 18/7 ǡRe(z) = 25/7 or -11/7 ˤʤޤ
Re(z) = 25/7 ξ
Re(z) + 1 = 32/7 ꡢϤޤȡ|Im(z)||Re(z) + 1||z + 1| = 345 ľѻѷǤ뤳Ȥʬꡢ
|z + 1| = 40/7 ǡMN = 1/2 * 6 * 40/7 = 120/7 cm Ǥ줬Ǥ
z = (25 + 24i)/7 ʤΤǡβž AOP 90̤ǡOAP ߳ѤǤ
Re(z) = -11/7 ξ
Re(z) + 1 = -4/7 ꡢϤޤȡϡʿȤʤȥʬꡢ
|z + 1| = sqrt((4/7)^2 + (24/7)^2) = 4/7 * sqrt(37) ǡMN = 12/7 * sqrt(37) cm Ǥ줬⤦ĤǤ
z = (-4 + 24i)/7 ʤΤǡβž AOP 90٤ĶOAP ϱԳѤǤ
ͥνȡ 818ڡ 22:17:56 MAIL:uchi@sco.bekkoame.ne.jp 25642
uchinyan
ʸ򸫤顢Ƥޤ
餷ޤ
ͥνȡ 818ڡ 17:57:23 MAIL:uchi@sco.bekkoame.ne.jp 25643
uchinyan
#25640
¤ϡǽ顢̤ˡϺƤΤǤ
äȡǽ˹ͤˡǤǤޤ

P AB ʿԤˤʤ褦AB = PC Ȥʤ C OP ˴ؤ Q ¦˼ޤ
APCB ʿԻշʤΤǡAP//BC Ǥ
ˡN AB ʿԤ BC Ȥθ D Ȥޤ餫ˡND = AB = 6 ǡD BC Ǥ
äơBCQ ˤϢꡢDM = 1/2 * CQ Ǥ
ơOAB OPQ ꡢOAB OPQ ˽Ťͤ A P ˰פޤǰưB C ˰פ褦˲žȡ
QPC βž = POA ȤʬꡢޤOA/OP = AB/PQ = PC/PQ ʤΤǡOAP PCQ Ǥ
ǡCQ/PC = AP/OA ǡCQ = AP/OA * PC = 30/7 * 6 = 180/7DM = 1/2 * 180/7 = 90/7 ˤʤޤ
ˡNMDONA ˤơ
MD//QCND//PC ꡢNDM = PCQ = OAPˡDM/DN = 90/7 * 1/6 = 15/7 = (1/2 * AP)/OA = NA/OA
ǡNMD ONA Ǥ
äơMN/MD = NO/NA ˤʤޤ
ǡP, N OA αĹ˿򲼤­ H, I Ȥޤ
OAP = 1/2 * OA * PH = 1/2 * 7 * PH = 84 ꡢPH = 24 ǡPAH ϡ345 ľѻѷʤΤǡAH = 18 Ǥ
ޤNI = 1/2 * PH = 12OI = OA + AI = OA + 1/2 * AH = 16 ꡢONA 345 ľѻѷǡNO = 20 Ǥ
ǡMN = NO/NA * MD = 20/15 * 90/7 = 120/7 cm

Ǥ⡢ONM OAB ȤϤ뤫˳ڤǤ (^^;
ͥνȡ 818ڡ 23:56:11 MAIL:uchi@sco.bekkoame.ne.jp 25644
X
ɤ̤ˤĤƸɤǤѤäȸǤMNƱΤϢPQȾʬʤȻפäɤ褯ߤȰ㤦Ǥ͡ǤPQȾʬˤʤΤAP,BQˤʤФʤˤʬ䤹ʤ̤ʤȤͤɤʤʤǡǤ⤳ʤȤʤäƹͤǤ礦͡Ȥ줳פޤ
819ʶ 11:37:48 25645
ϥ饮㡼ƥ
äȤǤޤɤ˥ߥäMATHEMATICA
ͭˤʤʤΤǶϫƤޤ
̶彣 819ʶ 13:50:38 HomePage:ĩ25646
tomh
#25633
ʤ󤬽Ф줿OAPԳѤξο (12/7)(37)
ǧޤ
ԡ 819ʶ 19:23:27 MAIL:tomh@yahoo.co.jp HomePage:H to M25647
ҡΤ
ޤκˢOABηϤɡǤɤȤ˵Ĥ
3A,B,P1ľˤȤꤷƹͤޤ
...ޤȤ˺ɸ򤪤Ʋ򤤤ʣʿ̤ʤˤΤǻ̤褦ʷ׻򤹤뱩ܤˤʤޤʾС
9ߤ濴 822ʷ 12:21:25 HomePage:25648
n
ΤäƤǤ͡ɤǷӤĤʤ櫓
824ʿ 5:45:02 25649