Difference between revisions of "2002 IMO Problems/Problem 2"

Revision as of 11:04, 7 October 2022

$\text{BC is a diameter of a circle center O. A is any point on the circle with } \angle AOC \not\le 60^\circ$

$\text{EF is the chord which is the perpendicular bisector of AO. D is the midpoint of the minor arc AB. The line through}$

$\text{O parallel to AD meets AC at J. Show that J is the incenter of triangle CEF.}$

$\text{By construction, AEOF is a rhombus with } 60^\circ - 120^\circ \text{angles}$

$\text{ Consequently, we may set } s = AO = AE = AF = EO = EF$

$\documentclass{imosol}$ (Error compiling LaTeX. Unknown error_msg)

\usepackage[pdftex]{graphicx} \begin{imosol} \includegraphics{imosol.png} \end{imosol}

@@ Line 7: / Line 7: @@
 :<math>\text{By construction, AEOF is a rhombus with } 60^\circ - 120^\circ \text{angles}</math>
 :<math>\text{ Consequently, we may set } s = AO = AE = AF = EO = EF</math>
-:<math>\documentclass{imosol}
+:<math>\documentclass{imosol}</math>
 \usepackage[pdftex]{graphicx}
 \begin{imosol}
 \includegraphics{imosol.png}
-\end{imosol}</math>
+\end{imosol}