# Difference between revisions of "2006 Cyprus MO/Lyceum/Problem 17"

## Problem

$AB\Gamma$ is equilateral triangle of side $\alpha$ and $A\Delta=BE=\frac{\alpha}{3}$. The measure of the angle $\ang \Gamma PE$ (Error compiling LaTeX. ! Undefined control sequence.) is

A. $60^{\circ}$

B. $50^{\circ}$

C. $40^{\circ}$

D. $45^{\circ}$

E. $70^{\circ}$

## Solution

Draw a segment $BF$ such that $BF = \frac{\alpha}{3}$. By symmetry we see the triangle in the middle is equilateral, so the measure of $\ang CPE = 60^{\circ} \ \mathrm{(A)}$ (Error compiling LaTeX. ! Undefined control sequence.).