# Curious Chord in a Circle

Geometry Level 5

$$A$$ and $$B$$ are points on the circumference of circle $$\Gamma$$. $$M$$ is the midpoint of the minor arc $$\stackrel{\frown}{AB}$$ and $$C$$ is a point on the circumference of $$\Gamma$$ such that it is between $$M$$ and $$B$$. $$D$$ is a point on the line segment $$AC$$ such that $$MD$$ is perpendicular to $$AC$$. If $$AD = 45$$ and $$BC = 15$$, what is the value of $$CD$$?

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