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[SPAM] [obm-l] Razão Máxima entre os lados de um Triângulo
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Content-Type: text/plain;
charset="Windows-1252"
Content-Transfer-Encoding: quoted-printable
Ol=E1 a todos!
Segue o problema extra=EDdo do livro Geometria II de A.C. Morgado, E. =
Wagner e M. Jorge=20
Em um tri=E2ngulo ABC, BC =3D 16 e h_a =3D 8, calcule a raz=E3o AB/AC, =
sabendo que ela =E9 m=E1xima.
Nota: h_a denota a altura relativa ao lado BC. O uso de derivada n=E3o =
=E9 permitido.
Com o aux=EDlio do Geogebra, verifiquei que a raz=E3o =E9 m=E1xima =
quando a altura (h_a) do tri=E2ngulo =E9 igual ao raio do c=EDrculo de =
Apolonius constru=EDdo sobre o lado BC, com o centro do c=EDrculo =
coincidindo com o p=E9 de h_a.=20
Pergunta: Como provar que a raz=E3o entre os lados AB e AC =E9 m=E1xima =
quando h_a =3D r, onde r =E9 o c=EDrculo de Apolonius, sem o uso de =
c=E1lculo?
Abra=E7os.
Ulysses Coelho de Souza.
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Content-Type: text/html;
charset="Windows-1252"
Content-Transfer-Encoding: quoted-printable
<!DOCTYPE HTML PUBLIC "-//W3C//DTD HTML 4.0 Transitional//EN">
<HTML><HEAD>
<META http-equiv=3DContent-Type content=3D"text/html; =
charset=3Dwindows-1252">
<META content=3D"MSHTML 6.00.6000.16587" name=3DGENERATOR>
<STYLE></STYLE>
</HEAD>
<BODY bgColor=3D#ffffff>
<DIV><FONT color=3D#000080 size=3D2>
<DIV><FONT color=3D#000080 size=3D2>
<DIV><FONT color=3D#000080>Ol=E1 a todos!</FONT></DIV>
<DIV><FONT color=3D#000080></FONT> </DIV>
<DIV><FONT color=3D#000080></FONT> </DIV>
<DIV><FONT color=3D#000080>Segue o problema extra=EDdo do livro =
Geometria II de=20
A.C. Morgado, E. Wagner e M. Jorge </FONT></DIV>
<DIV><FONT color=3D#000080></FONT> </DIV>
<DIV><FONT color=3D#000080><EM>Em um tri=E2ngulo ABC, BC =3D 16 e h_a =
=3D 8, calcule a=20
raz=E3o AB/AC, sabendo que ela =E9 m=E1xima.</EM></FONT></DIV>
<DIV><FONT color=3D#000080></FONT> </DIV>
<DIV><FONT color=3D#000080>Nota: h_a denota a altura relativa ao lado =
BC.=20
</FONT><FONT color=3D#000080>O uso de derivada n=E3o =E9 =
permitido.</FONT></DIV>
<DIV><FONT color=3D#000080></FONT> </DIV>
<DIV><FONT color=3D#000080></FONT> </DIV>
<DIV><FONT color=3D#000080>Com o aux=EDlio do Geogebra, =
verifiquei que a raz=E3o=20
=E9 m=E1xima quando a altura (h_a) do tri=E2ngulo =E9 igual ao raio =
do c=EDrculo de=20
Apolonius constru=EDdo sobre o lado BC, com o centro do c=EDrculo =
coincidindo com o=20
p=E9 de h_a. </FONT></DIV>
<DIV><FONT color=3D#000080></FONT> </DIV>
<DIV><FONT color=3D#000080>Pergunta: Como provar que a raz=E3o entre os =
lados AB e=20
AC =E9 m=E1xima quando h_a =3D r, onde r =E9 o c=EDrculo de Apolonius, =
sem o uso de=20
c=E1lculo?</FONT></DIV>
<DIV><FONT color=3D#000080></FONT> </DIV>
<DIV><FONT color=3D#000080>Abra=E7os.</FONT></DIV>
<DIV><FONT color=3D#000080></FONT> </DIV>
<DIV><FONT color=3D#000080>Ulysses Coelho de=20
Souza. </FONT></DIV></FONT></DIV></FONT></DIV></BODY></HTML>
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