Question

The length of the tangent from an external point P to a circle of radius 5 cm is 10 cm. The distance of the point from the centre of the circle is ______.

Answer 1

The length of the tangent from an external point P to a circle of radius 5 cm is 10 cm. The distance of the point from the centre of the circle is `underlinebb(sqrt(125)  cm)`.

Explanation:

Radius OT is perpendicular to the tangent at the point of contact, so triangle OTP is right-angled at T. 

Therefore by Pythagoras,

OP² = OT² + PT² 

= 5² + 10²

= 125

So OP = `sqrt(125) = 5sqrt(5)` cm.