similar triangles around a right triangle

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parmenides51

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parmenides51

#1 h Jul 29, 2018, 7:24 AM • 1 Y

Y by Adventure10

$ABC$ is a triangle with $\angle C = 90^o$ . $E$ is a point on $AC$ , and $F$ is the midpoint of $EC$ . $CH$ is an altitude. $I$ is the circumcenter of $AHE$ , and $G$ is the midpoint of $BC$ . Show that $ABC$ and $IGF$ are similar.

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PavelMath

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PavelMath

#2 h Jul 29, 2018, 9:03 AM • 1 Y

Y by Adventure10

parmenides51 wrote:

$ABC$ is a triangle with $\angle C = 90^o$ . $E$ is a point on $AC$ , and $F$ is the midpoint of $EC$ . $CH$ is an altitude. $I$ is the circumcenter of $AHE$ , and $G$ is the midpoint of $BC$ . Show that $ABC$ and $IGF$ are similar.

It is true only if $E$ is a midpoint of $AC$ ...

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parmenides51

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parmenides51

#3 h Jul 29, 2018, 11:22 AM • 2 Y

Y by Adventure10, Mango247

maybe I should have added the figure given, I though it was an easy figure to draw someone, it may contains more than those written in the text.

parmenides51 wrote:

$ABC$ is a triangle with $\angle C = 90^o$ . $E$ is a point on $AC$ , and $F$ is the midpoint of $EC$ . $CH$ is an altitude. $I$ is the circumcenter of $AHE$ , and $G$ is the midpoint of $BC$ . Show that $ABC$ and $IGF$ are similar.

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PavelMath

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PavelMath

#4 h Jul 29, 2018, 11:37 AM • 2 Y

Y by parmenides51, Adventure10

parmenides51 wrote:

maybe I should have added the figure given, I though it was an easy figure to draw someone, it may contains more than those written in the text.

parmenides51 wrote:

$ABC$ is a triangle with $\angle C = 90^o$ . $E$ is a point on $AC$ , and $F$ is the midpoint of $EC$ . $CH$ is an altitude. $I$ is the circumcenter of $AHE$ , and $G$ is the midpoint of $BC$ . Show that $ABC$ and $IGF$ are similar.

O... $I$ is the circumcenter, not incenter... Sorry...

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