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.]