Question

The length of tangent from a point A at a distance of 5 cm from the centre of the circle is 4 cm. What is the radius of the circle?

Answer 1

Given: OA = 5 cm (distance from centre O to point A); length of tangent AT = 4 cm.

Step-wise calculation:

1. Let T be the point of contact and r = OT be the radius. The tangent at T is perpendicular to the radius OT, so triangle OTA is right-angled at T.

2. Apply Pythagoras in right triangle OTA:

OA² = OT² + AT²

5² = r² + 4²

25 = r² + 16

r² = 9

r = 3 cm.

Radius of the circle = 3 cm.