in trapezoid ABCD base BC = 7cm, base AD = 14 cm, trapezoid diagonals intersecting at point O, and OC = 3cm. Find the AC.

Consider triangles AOD and BOC, they are similar (signs of similarity of triangles). Similarity coefficient k = 1/2, therefore, OC / AO = 1/2, AO = 2OC = 6; AC = 6 + 3 = 9

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