Line segments AB and CK intersect at point O, and the intersection is halved. It is known that AB = 6, CK = 8, AK = 5. Find BC.

At the intersection of the segments AB and CK at point O, the angle AOK is equal to the angle of the SOC, since when two straight lines intersect, the opposite angles are equal. Because by the condition of the problem, point O divides the segments AB and CK in half, which means AO = OB, CO = OK. According to the first sign of the equality of triangles, we have two equal triangles, which have two equal sides and an equal angle between these sides. In equal triangles, all sides are equal, respectively, the side of the AK and the side of the BC are equal to each other, i.e.

BC = AK = 5.

Answer: BC = 5.