Art of Problem Solving
AoPS Online
Math texts, online classes, and more
for students in grades 5-12.
Visit AoPS Online ‚
Books for Grades 5-12 Online Courses
Beast Academy
Engaging math books and online learning
for students ages 6-13.
Visit Beast Academy ‚
Books for Ages 6-13 Beast Academy Online
AoPS Academy
Small live classes for advanced math
and language arts learners in grades 2-12.
Visit AoPS Academy ‚
Find a Physical Campus Visit the Virtual Campus

1999 IMO Problems/Problem 5

Revision as of 20:44, 6 October 2023 by Tomasdiaz (talk | contribs) (Created page with "==Problem== Two circles <math>G_{1}</math> and <math>G_{2}</math> are contained inside the circle <math>G</math>, and are tangent to <math>G</math> at the distinct points <ma...")
(diff) ← Older revision | Latest revision (diff) | Newer revision → (diff)

Problem

Two circles $G_{1}$ and $G_{2}$ are contained inside the circle $G$, and are tangent to $G$ at the distinct points $M$ and $N$, respectively. $G_{1}$ passes through the center of $G_{2}$. The line passing through the two points of intersection of $G_{1}$ and $G_{2}$ meets $G$ at $A$ and $B$. The lines $MA$ and $MB$ meet $G_{1}$ at $C$ and $D$, respectively.

Prove that $CD$ is tangent to $G_{2}$.


Solution

This problem needs a solution. If you have a solution for it, please help us out by adding it.

Retrieved from "https://artofproblemsolving.com/wiki/index.php?title=1999_IMO_Problems/Problem_5&oldid=199276"