# 2014 USAJMO Problems/Problem 2

## Problem

Let $\triangle{ABC}$ be a non-equilateral, acute triangle with \$\angle A=60\textdegrees\$ (Error compiling LaTeX. ! Undefined control sequence.), and let $O$ and $H$ denote the circumcenter and orthocenter of $\triangle{ABC}$, respectively.

(a) Prove that line $OH$ intersects both segments $AB$ and $AC$.

(b) Line $OH$ intersects segments $AB$ and $AC$ at $P$ and $Q$, respectively. Denote by $s$ and $t$ the respective areas of triangle $APQ$ and quadrilateral $BPQC$. Determine the range of possible values for $s/t$.

## Solution

We draw a diagram to not lose points:

Part a

Part b