Perpendicular from excenter and midpoint of altitude

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Thanic Nur Samin
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Perpendicular from excenter and midpoint of altitude

Unread post by Thanic Nur Samin » Wed Mar 11, 2015 10:24 pm

Let $M$ be the midpoint of the altitude $BE$ in $\Delta ABC$ and suppose that the
excircle opposite $B$ touches $AC$ at $Y$ . Then the line $MY$ goes through the incenter $I$.

This problem is from 2009 geometry camp problem set. Hints would be more appreciated than complete solutions.
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Nirjhor
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Re: Perpendicular from excenter and midpoint of altitude

Unread post by Nirjhor » Wed Mar 11, 2015 11:27 pm

$1.$ Draw the diameter $GH$ of the incircle perpendicular to $AC$.

$2.$ Homothety.
If you still need help, read the first part of this.
- What is the value of the contour integral around Western Europe?

- Zero.

- Why?

- Because all the poles are in Eastern Europe.


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