ISL 2012 G4: angle biscector with circumcenter
- Thanic Nur Samin
- Posts:176
- Joined:Sun Dec 01, 2013 11:02 am
Let $ABC$ be a triangle with $AB$ and $AC$ not equal and circumcenter $O$. The bisector of $\angle BAC$ intersects $BC$ at $D$. Let $E$ be the reflection of $D$ with respect to the midpoint of $BC$. The lines through $D$ and $E$ perpendicular to $BC$ intersect the lines $AO$ and $AD$ at $X$ and $Y$ respectively. Prove that the quadrilateral $BXCY$ is cyclic.
Hammer with tact.
Because destroying everything mindlessly isn't cool enough.
Because destroying everything mindlessly isn't cool enough.
- Thanic Nur Samin
- Posts:176
- Joined:Sun Dec 01, 2013 11:02 am
Re: ISL 2012 G4: angle biscector with circumcenter
Hammer with tact.
Because destroying everything mindlessly isn't cool enough.
Because destroying everything mindlessly isn't cool enough.
Re: ISL 2012 G4: angle biscector with circumcenter
A synthetic solution:
"Questions we can't answer are far better than answers we can't question"
Re: ISL 2012 G4: angle biscector with circumcenter
The first principle is that you must not fool yourself and you are the easiest person to fool.