Reflection of C is on AB

Geometry Level 2

A right angle triangle \(ABC\) is such that \(AC=24\)cm, \(CB=10\)cm and \( \angle ACB=90^{\circ}\). A point \(D\) on \(CB\) is such that when point \(C\) is reflected upon line \(AD\), the reflected point will be on line \(AB\). The length of \(CD=\frac{a}{b}\) where \(a\) and \(b\) are coprime integers. Find the value of \(a+b\).

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