In the given figure, PT is tangent to the circle at T. If $P A = 4 cm$ and $AB = 5 cm,$ find PT.

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3 cm

12 cm

9 cm

6 cm

answer is B.

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Detailed Solution

Given that PT is tangent to the circle at T and

P A = 4 cm

and

AB = 5 cm .

We have to find the length of PT.
Question Image

If a tangent and a secant are drawn to a circle from an external point, then the square of the distance between the external point and the point at which tangent intersects the circle is the same as the product of the internal and external secant segment.
Here,

P A = 4 cm

and

A B = 5 cm

Therefore,

P B = 4 + 5 ⇒ P B = 9 cm

Since a tangent and a secant is drawn to a circle from an external point then the square of the distance between the external point and the point at which tangent intersect the circle is the same as the product of the internal and external secant segment,