Question

In Fig., $O$ is the centre of a circle of radius 5 cm. $T$ is a point such that $OT = 13$ cm and $OT$ intersects circle at $E$. If $AB$ is a tangent to the circle at $E$, find the length of $AB$, where $TP$ and $TQ$ are two tangents to the circle.

Answer 1

20/3 cm

Answer 2

The solution uses coordinate geometry to solve the problem. It places the circle at the origin and finds the equations of the tangents from point T to the circle. Then, it finds the intersection points of these tangents with the tangent at point E. Finally, it calculates the distance between these intersection points to find the length of AB.