In figure, O is the center 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.

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5.3 cm

3.3 cm

4.3 cm

6.3 cm

answer is A.

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Detailed Solution

Given that O is the center of a circle of radius 5 cm. T is a point such that

OT = 13 cm

and

OT

intersects circle at E.
We have to find the length of AB.
Question Image

By Pythagoras theorem, for a right-angled triangle ,

A B C, A C 2 = A B 2 + B C 2

, where AC is the hypotenuse of

△ A B C

Given: O is the center of a circle of radius 5cm. T is a point such that OT = 13cm and OT intersects circle at E. If AB is a tangent to the circle at E. To Find: Find the length of AB where TP and TQ are two tangents to the circle.
From the right angle triangle POT,