The isosceles triangle $\triangle ABC$, with $AB=AC$, is inscribed in the circle $\omega$. Let $P$ be a variable point on the arc $\stackrel{\frown}{BC}$ that does not contain $A$, and let $I_B$ and $I_C$ denote the incenters of triangles $\triangle ABP$ and $\triangle ACP$, respectively.

Prove that as $P$ varies, the circumcircle of triangle $\triangle PI_BI_C$ passes through a fixed point.

WARNING: DON'T USE GEOGEBRA

## When everyone is busy solving USA(J)MO 2017,I am solving2016

- Thamim Zahin
**Posts:**98**Joined:**Wed Aug 03, 2016 5:42 pm

### When everyone is busy solving USA(J)MO 2017,I am solving2016

I think we judge talent wrong. What do we see as talent? I think I have made the same mistake myself. We judge talent by the trophies on their showcases, the flamboyance the supremacy. We don't see things like determination, courage, discipline, temperament.

- Atonu Roy Chowdhury
**Posts:**40**Joined:**Fri Aug 05, 2016 7:57 pm**Location:**Chittagong, Bangladesh

### Re: When everyone is busy solving USA(J)MO 2017,I am solving

Solution with angle chasing only. But seems ugly to me.