The length of the tangent PA from a point P to a circle of radius 3 cm is 4 cm. The distance of A from the centre of the circle is : (A) 5 cm (B) 7 cm (C) 25 cm (D) 7 cm

The length of the tangent PA from a point P to a circle of radius 3cm is 4 cm.The distance of A from the centre of the circle is?

SOLUTION: Let C be the centre of the circle.

In the above figure, we have the following information

RadiusPC =3 cm andPA= 4 cm

As we know that the tangent drawn at any point ( like pointP) of the circle from outer side ( like pointA )makes right angle with diametric line.

∴In ΔAPCis right angleΔ.

Using Pythagoras theorem

Hence, The distance of A from the centre of the circle = 5 cm