1999 IMO Problems/Problem 5


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 $G_{2}$.


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See Also

1999 IMO (Problems) • Resources
Preceded by
Problem 4
1 2 3 4 5 6 Followed by
Problem 6
All IMO Problems and Solutions