he length of a tangent drawn from a point at a distance of 29 cm from centre of the circle is 20 cm. The radius of the circle is

The problem involves a right triangle formed by the radius, the tangent line, and the line from the center of the circle to the point from which the tangent is drawn.

Step 1: Identify the right triangle. The radius of the circle is perpendicular to the tangent at the point of tangency, forming a right triangle.

Step 2: Apply the Pythagorean theorem. The Pythagorean theorem states that in a right triangle, the square of the length of the hypotenuse (the side opposite the right angle) is equal to the sum of the squares of the lengths of the other two sides. Here, the hypotenuse is the line from the center of the circle to the point from which the tangent is drawn (29 cm), one side is the radius of the circle (which we're trying to find), and the other side is the tangent line (20 cm).

Step 3: Solve for the radius. Using the Pythagorean theorem, we have:

(29 cm)^2 = (radius)^2 + (20 cm)^2

Solving for the radius, we get:

(radius)^2 = (29 cm)^2 - (20 cm)^2 (radius)^2 = 841 cm^2 - 400 cm^2 (radius)^2 = 441 cm^2

Taking the square root of both sides, we find that the radius is √441 cm = 21 cm.

So, the radius of the circle is 21 cm.