5. PYQ - Similar triangle

In the adjoining figure, \(\Delta CAB\) is a right triangle, right angled at \(A\) and \(AD \perp BC\). Prove that \(\Delta ADB \sim \Delta CDA\). Further, if \(BC = 10 \ cm\) and \(CD = 1 \ cm\), calculate the length of \(AD\). 

 

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​$\mathit{AD}=i\mathit{cm}$