A Weird Cut Of Concentric Circles

Geometry Level 3

In the figure above, the circles are concentric with centre \(O\). \(B\) is a point on the larger circle. \(D\) is a point on the smaller circle. \(BD\) is joined, provided that \(BD\) touches the circle at only one point. Now \(OB\) is joined and extended to meet the larger circle at \(A\). Find the distance between points \(A\) and \(D\) if the radii of the circles are \(4\sqrt{13}\) and \(8\) units respectively.

Clarification: Concentric circles are circles with a common centre.

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