## [ Product of lengths of chord segments and lengths of secant segments

 Pythagorean Theorem (direct and inverse). [Cyclic quadrilateral with perpendicular diagonals] The diagonals $A C$ and $B D$ of the cyclic quadrilateral $A B C D$ are perpendicular to each other and intersect at point $M$. It is known that $A M=3, B M=4$ and $C M=6$. Find $C D$.

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Apply the theorem of the products of segments of intersecting chords and the Pythagorean theorem.

## Answer

7.5 .