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[SPAM] [obm-l] Re: [obm-l] geometria olimpíada

To: <obm-l@xxxxxxxxxxxxxx>
Subject: [SPAM] [obm-l] Re: [obm-l] geometria olimpíada
From: "Anderson Weber" <andersweber@xxxxxxxxxx>
Date: Wed, 9 Apr 2008 23:30:40 -0300
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Ol=E1

Uma dica para a solu=E7=E3o: note que o ponto R =E9 equidistante da reta =
s e do lado CD. Portanto, R pertence =E0 bissetriz do =E2ngulo DVT.

Uma outra maneira de resolver esse lindo problema...

prolongue o lado AD at=E9 obter P na intersec=E7=E3o com a reta s.
prolongue o lado CB at=E9 obter K na intersec=E7=E3o com a reta r.

Note que o quadril=E1tero SPTK =E9 um quadril=E1tero not=E1vel (losango) =
- isso pode ser provado por congru=EAncia entre tri=E2ngulos.

Um abra=E7o

Anderson Weber

  ----- Original Message -----=20
  From: Jo=E3o Gabriel Preturlan=20
  To: obm-l@xxxxxxxxxxxxxx=20
  Sent: Tuesday, April 08, 2008 5:00 PM
  Subject: [obm-l] geometria olimp=EDada


  Sauda=E7=F5es!

  =20

  Gostaria que voc=EAs me ajudassem neste problema.

  =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."

  =20



  =20

  Agrade=E7o muito pela ajuda.

  =20

  JG.

  =20

  =20



  No virus found in this outgoing message.
  Checked by AVG.
  Version: 7.5.519 / Virus Database: 269.22.10/1366 - Release Date: =
08/04/2008 17:03



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<DIV><FONT face=3DArial size=3D2>Ol=E1</FONT></DIV>
<DIV><FONT face=3DArial size=3D2></FONT>&nbsp;</DIV>
<DIV><FONT face=3DArial size=3D2>Uma dica para a solu=E7=E3o: note que o =
ponto R =E9=20
equidistante da reta s e do lado CD. Portanto, R pertence =E0 bissetriz =
do =E2ngulo=20
DVT.</FONT></DIV>
<DIV><FONT face=3DArial size=3D2></FONT>&nbsp;</DIV>
<DIV><FONT face=3DArial size=3D2>Uma outra maneira de resolver esse =
lindo=20
problema...</FONT></DIV>
<DIV><FONT face=3DArial size=3D2></FONT>&nbsp;</DIV>
<DIV><FONT face=3DArial size=3D2>prolongue o lado AD at=E9 obter P na =
intersec=E7=E3o com=20
a reta s.</FONT></DIV>
<DIV><FONT face=3DArial size=3D2>prolongue o lado CB at=E9 obter K na =
intersec=E7=E3o com=20
a reta r.</FONT></DIV>
<DIV><FONT face=3DArial size=3D2></FONT>&nbsp;</DIV>
<DIV><FONT face=3DArial size=3D2>Note que o quadril=E1tero SPTK =E9 um =
quadril=E1tero=20
not=E1vel (losango) - isso pode ser provado por congru=EAncia entre=20
tri=E2ngulos.</FONT></DIV>
<DIV><FONT face=3DArial size=3D2></FONT>&nbsp;</DIV>
<DIV><FONT face=3DArial size=3D2>Um abra=E7o</FONT></DIV>
<DIV><FONT face=3DArial size=3D2></FONT>&nbsp;</DIV>
<DIV><FONT face=3DArial size=3D2>Anderson Weber</FONT></DIV>
<DIV><FONT face=3DArial size=3D2></FONT>&nbsp;</DIV>
<BLOCKQUOTE dir=3Dltr=20
style=3D"PADDING-RIGHT: 0px; PADDING-LEFT: 5px; MARGIN-LEFT: 5px; =
BORDER-LEFT: #000000 2px solid; MARGIN-RIGHT: 0px">
  <DIV style=3D"FONT: 10pt arial">----- Original Message ----- </DIV>
  <DIV=20
  style=3D"BACKGROUND: #e4e4e4; FONT: 10pt arial; font-color: =
black"><B>From:</B>=20
  <A title=3Djgpreturlan@xxxxxxxxxx =
href=3D"mailto:jgpreturlan@xxxxxxxxxx";>Jo=E3o=20
  Gabriel Preturlan</A> </DIV>
  <DIV style=3D"FONT: 10pt arial"><B>To:</B> <A =
title=3Dobm-l@xxxxxxxxxxxxxx=20
  href=3D"mailto:obm-l@xxxxxxxxxxxxxx";>obm-l@xxxxxxxxxxxxxx</A> </DIV>
  <DIV style=3D"FONT: 10pt arial"><B>Sent:</B> Tuesday, April 08, 2008 =
5:00=20
  PM</DIV>
  <DIV style=3D"FONT: 10pt arial"><B>Subject:</B> [obm-l] geometria=20
olimp=EDada</DIV>
  <DIV><BR></DIV>
  <DIV class=3DSection1>
  <P class=3DMsoNormal>Sauda=E7=F5es!<o:p></o:p></P>
  <P class=3DMsoNormal><o:p>&nbsp;</o:p></P>
  <P class=3DMsoNormal>Gostaria que voc=EAs me ajudassem neste=20
  problema.<o:p></o:p></P>
  <P class=3DMsoNormal><o:p>&nbsp;</o:p></P>
  <P class=3DMsoNormal>=93Se as retas r e s s=E3o paralelas e distam L =
entre si e o=20
  quadrado ABCD tem lado L tamb=E9m, prove que o =E2ngulo S=D4R tem 45=20
  graus.=94<o:p></o:p></P>
  <P class=3DMsoNormal><o:p>&nbsp;</o:p></P>
  <P class=3DMsoNormal><IMG id=3DImagem_x0020_2 height=3D162=20
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width=3D294><o:p></o:p></P>
  <P class=3DMsoNormal><o:p>&nbsp;</o:p></P>
  <P class=3DMsoNormal>Agrade=E7o muito pela ajuda.<o:p></o:p></P>
  <P class=3DMsoNormal><o:p>&nbsp;</o:p></P>
  <P class=3DMsoNormal>JG.<o:p></o:p></P>
  <P class=3DMsoNormal><SPAN=20
  style=3D"FONT-SIZE: 12pt; FONT-FAMILY: 'Times New =
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  <P><FONT size=3D2>No virus found in this outgoing message.<BR>Checked =
by=20
  AVG.<BR>Version: 7.5.519 / Virus Database: 269.22.10/1366 - Release =
Date:=20
  08/04/2008 17:03<BR></FONT></P>
  <P><FONT face=3DArial size=3D2></FONT></P></BLOCKQUOTE></BODY></HTML>

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