If the length of tangent from a point Aat a distance of 26 cm from the centre ofthe circle is 10 cm, then the radius ofthe circle is:

The problem involves a circle and a tangent line from a point outside the circle. In such a scenario, the tangent line is perpendicular to the radius of the circle at the point of tangency. This forms a right-angled triangle with the radius, the tangent line, and the line segment from the center of the circle to the point outside the circle.

Here are the steps to solve the problem:

1. Identify the given values: The distance from the point to the center of the circle (the hypotenuse of the right triangle) is 26 cm, and the length of the tangent (one of the sides of the right triangle) is 10 cm.

2. Use the Pythagorean theorem to solve for the radius (the other side of the right triangle). The Pythagorean theorem states that the square of the hypotenuse is equal to the sum of the squares of the other two sides. In this case, it can be written as: (radius)^2 = (26 cm)^2 - (10 cm)^2.

3. Calculate the square of 26 cm and 10 cm: (26 cm)^2 = 676 cm^2 and (10 cm)^2 = 100 cm^2.

4. Subtract the square of 10 cm from the square of 26 cm to find the square of the radius: (radius)^2 = 676 cm^2 - 100 cm^2 = 576 cm^2.

5. Take the square root of 576 cm^2 to find the radius: radius = √576 cm^2 = 24 cm.

So, the radius of the circle is 24 cm.