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[SPAM] [obm-l] RES: [obm-l] Re: [obm-l] geometria olimpíada
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Esta é uma mensagem em várias partes no formato MIME.
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Ol=E1!
=20
Obrigado pela dica.... foi de grande ajuda!
mas realmente queria saber de onde o Saulo tirou a rela=E7=E3o da =
primeira linha
da resolu=E7=E3o dele estou tentando encontr=E1-la mas n=E3o tenho =
progresso. Se
algu=E9m puder me explicar eu agrade=E7o imensamente.
=20
tagx/2=3Drq2-1=3Drq(1-cosx)/(1+cosx) (n=E3o consigo sacar de que lugar =
vem esta
rela=E7=E3o)
(1-w)/(1+w)=3D2-2rq2+1=3D3-2rq2
3-2rq2-1=3D-w(4-2rq2)
w=3D-(1-rq2)/(2-rq2)=3D-(2+rq2-2rq2-2)/2=3Drq2/2
x=3D45=BA
=20
"Se as retas r e s s=E3o paralelas e distam L entre si e o quadrado ABCD =
tem
lado L tamb=E9m, prove que o =E2ngulo S=D4R tem 45 graus."
cid:image001.png@01C89999.99F2A080
=20
=20
De: owner-obm-l@xxxxxxxxxxxxxx [mailto:owner-obm-l@xxxxxxxxxxxxxx] Em =
nome
de Arconcher
Enviada em: quarta-feira, 9 de abril de 2008 17:25
Para: obm-l@xxxxxxxxxxxxxx
Assunto: [obm-l] Re: [obm-l] geometria olimp=EDada
=20
Sendo a largura da faixa igual ao lado do quadrado fica f=E1cil de =
perceber
que as linhas TS e VR s=E3o bissetrizes dos =E2ngulos obtusos formados =
entre um
lado do quadrado e uma das retas da faixa, por exemplo: do ponto S baixe
perpendiculares ao lado AB do quadrado e =E0 reta suporte de VT, tais
segmentos perpendiculares medem L da=ED TS =E9 bissetriz do =E2ngulo =
VTB. De modo
an=E1logo para os pontos
R,T e V . A=ED fica bem f=E1cil concluir que SOR mede 45=BA.
Agora mostre que a soma dos per=EDmetros dos tri=E2ngulos
ASR e VTC =E9 constante ( Asian Pasific , n=E3o me lembro do ano ). Use =
as
bissetrizes anteriores que sai f=E1cil.
Saludos.
Arconcher
=20
No virus found in this incoming message.
Checked by AVG.
Version: 7.5.519 / Virus Database: 269.22.10/1367 - Release Date: =
09/04/2008
07:10
No virus found in this outgoing message.
Checked by AVG.=20
Version: 7.5.519 / Virus Database: 269.22.10/1367 - Release Date: =
09/04/2008
07:10
=20
=20
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<p class=3DMsoNormal><span =
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color:#1F497D'>Ol=E1!<o:p></o:p></span></p>
<p class=3DMsoNormal><span =
style=3D'font-size:11.0pt;font-family:"Calibri","sans-serif";
color:#1F497D'><o:p> </o:p></span></p>
<p class=3DMsoNormal><span =
style=3D'font-size:11.0pt;font-family:"Calibri","sans-serif";
color:#1F497D'>Obrigado pela dica.... foi de grande =
ajuda!<o:p></o:p></span></p>
<p class=3DMsoNormal><span =
style=3D'font-size:11.0pt;font-family:"Calibri","sans-serif";
color:#1F497D'>mas realmente queria saber de onde o Saulo tirou a =
rela=E7=E3o da
primeira linha da resolu=E7=E3o dele estou tentando encontr=E1-la mas =
n=E3o tenho
progresso. Se algu=E9m puder me explicar eu agrade=E7o =
imensamente.<o:p></o:p></span></p>
<p class=3DMsoNormal><span =
style=3D'font-size:11.0pt;font-family:"Calibri","sans-serif";
color:#1F497D'><o:p> </o:p></span></p>
<p class=3DMsoNormal><b>tagx/2=3Drq2-1=3Drq(1-cosx)/(1+cosx) (n=E3o =
consigo sacar de
que lugar vem esta rela=E7=E3o)<o:p></o:p></b></p>
<p class=3DMsoNormal>(1-w)/(1+w)=3D2-2rq2+1=3D3-2rq2<o:p></o:p></p>
<p class=3DMsoNormal>3-2rq2-1=3D-w(4-2rq2)<o:p></o:p></p>
<p =
class=3DMsoNormal>w=3D-(1-rq2)/(2-rq2)=3D-(2+rq2-2rq2-2)/2=3Drq2/2<o:p></=
o:p></p>
<p class=3DMsoNormal =
style=3D'margin-bottom:12.0pt'>x=3D45=BA<o:p></o:p></p>
<p class=3DMsoNormal><span =
style=3D'font-size:11.0pt;font-family:"Calibri","sans-serif";
color:#1F497D'><o:p> </o:p></span></p>
<p>"Se as retas r e s s=E3o paralelas e distam L entre si e o =
quadrado ABCD
tem lado L tamb=E9m, prove que o =E2ngulo S=D4R tem 45 =
graus."<o:p></o:p></p>
<p class=3DMsoNormal><span =
style=3D'font-size:11.0pt;font-family:"Calibri","sans-serif";
color:#1F497D'><img width=3D294 height=3D162 id=3D"Imagem_x0020_1"
src=3D"cid:image001.png@01C89A90.9D216A00"
alt=3D"cid:image001.png@01C89999.99F2A080"></span><span =
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color:#1F497D'><o:p> </o:p></span></p>
<p class=3DMsoNormal><span =
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<div>
<div style=3D'border:none;border-top:solid #B5C4DF 1.0pt;padding:3.0pt =
0cm 0cm 0cm'>
<p class=3DMsoNormal><b><span =
style=3D'font-size:10.0pt;font-family:"Tahoma","sans-serif"'>De:</span></=
b><span
style=3D'font-size:10.0pt;font-family:"Tahoma","sans-serif"'>
owner-obm-l@xxxxxxxxxxxxxx [mailto:owner-obm-l@xxxxxxxxxxxxxx] <b>Em =
nome de </b>Arconcher<br>
<b>Enviada em:</b> quarta-feira, 9 de abril de 2008 17:25<br>
<b>Para:</b> obm-l@xxxxxxxxxxxxxx<br>
<b>Assunto:</b> [obm-l] Re: [obm-l] geometria =
olimp=EDada<o:p></o:p></span></p>
</div>
</div>
<p class=3DMsoNormal><o:p> </o:p></p>
<div>
<p class=3DMsoNormal><span =
style=3D'font-size:10.0pt;font-family:"Arial","sans-serif"'>Sendo
a largura da faixa igual ao lado do quadrado fica f=E1cil de perceber =
que as
linhas TS e VR s=E3o bissetrizes dos =E2ngulos obtusos formados entre um =
lado do
quadrado e uma das retas da faixa, por exemplo: do ponto S baixe
perpendiculares ao lado AB do quadrado e =E0 reta suporte de VT, tais =
segmentos
perpendiculares medem L da=ED TS =E9 bissetriz do =E2ngulo VTB. De modo =
an=E1logo para
os pontos</span><o:p></o:p></p>
</div>
<div>
<p class=3DMsoNormal><span =
style=3D'font-size:10.0pt;font-family:"Arial","sans-serif"'>R,T
e V . A=ED fica bem f=E1cil concluir que SOR mede =
45=BA.</span><o:p></o:p></p>
</div>
<div>
<p class=3DMsoNormal><span =
style=3D'font-size:10.0pt;font-family:"Arial","sans-serif"'>Agora
mostre que a soma dos per=EDmetros dos =
tri=E2ngulos</span><o:p></o:p></p>
</div>
<div>
<p class=3DMsoNormal><span =
style=3D'font-size:10.0pt;font-family:"Arial","sans-serif"'>ASR
e VTC =E9 constante ( Asian Pasific , n=E3o me lembro do ano ). Use as =
bissetrizes
anteriores que sai f=E1cil.</span><o:p></o:p></p>
</div>
<div>
<p class=3DMsoNormal><span =
style=3D'font-size:10.0pt;font-family:"Arial","sans-serif"'>Saludos.</spa=
n><o:p></o:p></p>
</div>
<div>
<p class=3DMsoNormal><span =
style=3D'font-size:10.0pt;font-family:"Arial","sans-serif"'>Arconcher</sp=
an><o:p></o:p></p>
</div>
<p class=3DMsoNormal><o:p> </o:p></p>
<p><span style=3D'font-size:10.0pt'>No virus found in this incoming =
message.<br>
Checked by AVG.<br>
Version: 7.5.519 / Virus Database: 269.22.10/1367 - Release Date: =
09/04/2008
07:10</span><o:p></o:p></p>
</div>
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<BR>
<P><FONT SIZE=3D2>No virus found in this outgoing message.<BR>
Checked by AVG.<BR>
Version: 7.5.519 / Virus Database: 269.22.10/1367 - Release Date: =
09/04/2008 07:10<BR>
</FONT> </P>
<P><FONT SIZE=3D2 FACE=3D"Arial"> </FONT> </P>
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Instruções para entrar na lista, sair da lista e usar a lista em
http://www.mat.puc-rio.br/~obmlistas/obm-l.html
=========================================================================