Reflection of C is on AB

Geometry Level 2

A right angle triangle ABCABC is such that AC=24AC=24cm, CB=10CB=10cm and ACB=90 \angle ACB=90^{\circ}. A point DD on CBCB is such that when point CC is reflected upon line ADAD, the reflected point will be on line ABAB. The length of CD=abCD=\frac{a}{b} where aa and bb are coprime integers. Find the value of a+ba+b.

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