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1999 IMO Problems/Problem 5

Revision as of 19:44, 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...")
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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

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