A tangent PQ at a point P of a circle of radius 6 cm meets a line through the Centre O at a point Q, so that OQ=10 cm. The length of tangent PQ is ______.

Given:

Radius OP = 6 cm

OQ = 10 cm

PQ is the tangent to the circle.

To find: Length of tangent PQ

Explanation:

In this case, the radius of the circle, OP, and the line OQ form a right triangle with the tangent PQ. According to the Pythagorean theorem, the square of the length of the hypotenuse (OQ) is equal to the sum of the squares of the other two sides (OP and PQ).

Using the Pythagoras theorem: 
OQ² = OP² + PQ²

Substitute the given values:

10² = 6² + PQ²

100 = 36 + PQ²

PQ² = 100 - 36

PQ² = 64

PQ = 8 cm