Let the radius of the circle be r.

The line from the center O to the point of tangency T (where the tangent meets the circle) is perpendicular to the tangent line PT at the point of tangency. Thus, we have a right-angled triangle OTP, where:

• OT = r (the radius of the circle),
• PT = 10 cm (the length of the tangent),
• OP = 26 cm (the distance from the point P to the center O).

Using the Pythagorean theorem:

OP² = OT² + PT²

Substitute the known values:

26² = r² + 10²

Simplify the equation:

676 = r² + 100

Now, solve for r²:

r² = 676 – 100 = 576

Finally, take the square root of both sides:

r = √576 = 24 cm

Thus, the length of the radius of the circle is 24 cm.