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

Revision as of 11:01, 7 October 2022

Problem

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

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

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

Solution

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

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

$\documentclass{article} \usepackage{graphicx} \begin{document} \includegraphics{imosol.png} \end{document}$ (Error compiling LaTeX. Unknown error_msg)

@@ 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{article} \usepackage[pdftex]{graphicx} \begin{document} \includegraphics{imosol.png} \end{document}</math>
+:<math>\documentclass{article} \usepackage{graphicx} \begin{document} \includegraphics{imosol.png} \end{document}</math>

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

Revision as of 11:01, 7 October 2022

Problem

Solution