The diagonals of the trapezoid ABCD with bases AB and CD meet at point O. Find AB if OB = 4 OD = 10 DC = 25.

In triangles AOB and СOD, the angle AOB is equal to СOD as the vertical angles at the intersection of the diagonals AC and ВD. The angle OAB is equal to the angle of the OСD as criss-crossing angles at the intersection of parallel straight lines AB and СD of the secant AC.

Then triangle AOB is similar to triangle СOD in two angles.

Let’s determine the coefficient of similarity of triangles.

K = OB / OD = 4/10 = 2/5.

Then AB / SD = 2/5.

AB = 2 * СD / 5 = 2 * 25/5 = 10 cm.

Answer: The length of the base AB is 10 cm.