Find the length of the CO segment if it is known in the trapezoid: MO = 12 KP = 20 CK = 16.

Let us prove that the MCO triangle is similar to the DAC triangle.

Angle МСО = КСР as vertical angles at the intersection of diagonals МР and ОК.

Angle СОМ = СКР as criss-crossing angles at the intersection of parallel straight lines MO and KR secant OK.

Then the triangles MCO and DAC are similar in two angles.

Let’s determine the coefficient of similarity of triangles.

K = OM / KР 12/20 = 3/5.

Then CO / CK = 3/5.

CO = 3 * CK / 5 = 3 * 16/5 = 9.6 cm.

Answer: The length of the CO segment is 9.6 cm.