O is the centre of a circle of radius 5cm. T is a point such that OT=13cm and OT intersects the circle at E. If AB is the tangent to the circle at E, find length of AB.

Explanation

Given: `angle OPT=90^circ`


Applying Pythagoras in `triangle OPT`,


`OT^2=OP^2+PT^2`


`Rightarrow quad 13^2=5^2+PT^2 `
`Rightarrow quad PT^2=169-25=144 `


`Rightarrow quad PT=12 cm`


Since lengths of tangents drawn from a point to a circle are equal. So,


`AP=AE=x`(assume)


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