11. Find the length of the required tangent

\(TP\) and \(TQ\) are two tangents from the point \(T\) to the circle having its centre at \(O\). \(AB\) is another tangent touching the circle externally at \(E\) intersecting \(TP\) at \(A\) and \(TO\) at \(Q\). If the radius of the circle is 36 \(cm\) and the length of \(OT\) passing through \(E\) is 85 \(cm\), determine the length of \(AB\).

 

Answer:

 

The length of \(AB\) is  \(cm\).

 

[Note: If the answer is a whole number, enter as it is. If not, enter the answer up to one decimal place.]