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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