# Can you generalise this?

Geometry Level 4

Suppose that $$A$$, $$B$$ and $$M$$ are points on a circle such that $$M$$ is the midpoint of arc $$AB$$. Let $$C$$ be an arbitrary point on the arc $$AMB$$ such that $$AC$$ is longer than $$BC$$. Let $$D$$ be the foot of the perpendicular from $$M$$ to $$AC$$.

If the length of $$DC$$ is 5 and the length of $$BC$$ is 2, find the length of $$AD$$.

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