Given is \(\triangle ABC\) of side length \(10\). \(\triangle ABD\) is a right angle triangle with \(\overline { AD } \) as its hypotenuse. The value of \(\overline { BD } \) such that \(\overline { BC } \bot \overline { AD } \) is \(\ell \). Find \(\left\lceil \ell \right\rceil \).

Note:\(\left\lceil x \right\rceil \) represents the smallest integer greater than or equal to \(x\).

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