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.
Perpendicular from excenter and midpoint of altitude
- Thanic Nur Samin
- Posts:176
- Joined:Sun Dec 01, 2013 11:02 am
Hammer with tact.
Because destroying everything mindlessly isn't cool enough.
Because destroying everything mindlessly isn't cool enough.
Re: Perpendicular from excenter and midpoint of altitude
$1.$ Draw the diameter $GH$ of the incircle perpendicular to $AC$.
$2.$ Homothety.
$2.$ Homothety.
- What is the value of the contour integral around Western Europe?
- Zero.
- Why?
- Because all the poles are in Eastern Europe.
Revive the IMO marathon.
- Zero.
- Why?
- Because all the poles are in Eastern Europe.
Revive the IMO marathon.