1999 IMO Problems/Problem 5

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

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