Through point M, 20 cm away from the center of the circle, a tangent MK

Through point M, 20 cm away from the center of the circle, a tangent MK is drawn to it (K is the point of tangency) The radius of the circle is 12 cm. Calculate the length of the tangent MK

From point O, the center of the circle, draw the radius OK to the point of tangency.

Since the OK radius is drawn to the tangency point, this radius is perpendicular to the tangent MK, and then the OKM triangle is rectangular.

In a right-angled triangle OKM, according to the Pythagorean theorem, we determine the length of the leg MK.

MK ^ 2 = OM ^ 2 – OK ^ 2 = 20 ^ 2 – 12 ^ 2 = 400 – 144 = 256.

MK = 16 cm.

Answer: The length of the tangent is 16 cm.