In trapezoid ABCD BC, diagonals parallel to AD intersect at point O, the area of triangle BOC-3

In trapezoid ABCD BC, diagonals parallel to AD intersect at point O, the area of triangle BOC-3, and the area of triangle AOD-27, find AC If AO-6.

The triangles AOC and BOC are similar in the third similarity feature, since the angle AOD = angle BOC (as vertical), the angles OBC = ODA and OAD = OCB as crosswise at the intersection of the parallel sides of the trapezoid with a diagonal.
The ratio of the areas of similar triangles is equal to the square of the similarity coefficient, that is, k ^ 2 = 27/3 = 9, k = 3. To find the side of the OC, you need to divide the AO by the similarity coefficient. OC = 6/3 = 2.
Answer: AC = AO + OC = 6 + 2 = 8