The tangents MN and KN are drawn through the points M and K lying on the circle with center O.

The tangents MN and KN are drawn through the points M and K lying on the circle with center O. Prove that triangle MON = triangle KON.

Draw the radii of the circle OK and OM to the points of contact K and M, and connect the point N to the center of the circle.

According to the properties of the tangent, the radii drawn to the point of tangency are perpendicular to the tangent.

Then the triangles OKN and OMN are rectangular, in which the hypotenuse ON is common and the legs OK and OM are equal as the radii of the circle. Consequently, the triangles OKN and OMN are equal in leg and hypotenuse, as required.