MN and MK-line segments of tangents drawn to a circle of radius 5 cm Find MN and MK if MO = 13 cm

From the point O, the center of the circle, we will construct the radii OH and OK to the points of tangency.

By the property of the tangent, the radius drawn to the tangency point is perpendicular to the tangent itself, then the MOH triangle is rectangular.

By the Pythagorean theorem, we determine the length of the leg MH.

MH ^ 2 = MO ^ 2 – OH ^ 2 = 169 – 25 = 144.

MH = 12 cm.

The tangent MH and MK are drawn from the same point, then MK = MH = 12 cm.

Answer: The length of the tangents is 12 cm.

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