Equal chords MK and NL are drawn in a circle on opposite sides of the diameter MN. Prove that MK || NL.

Let’s connect the points M and L, as well as K and N. By condition, MN is the diameter of the circle, then the inscribed angles MKN and MLN are straight lines, since they are based on the diameter of the circle.

Right-angled triangles MKN and MLN are equal in common hypotenuse and equal legs LN and MK.

Then the angle KMN = LMN, the angle NML = MNK. The sum of the acute angles of a right-angled triangle is 90, then the angle KMN + KLN = 900, and therefore the quadrilateral MKNL is a rectangle, which means that MK are parallel to NL, which was required to prove.