Trapezoid ABCD AD and BC are the bases, AC and BD are the diagonals, O is the intersection point of the diagonals.

Trapezoid ABCD AD and BC are the bases, AC and BD are the diagonals, O is the intersection point of the diagonals. It is known that AD = 6 m, BC = 3 m, AO = 4 m. Find OC.

Let us prove that the triangles BOС and AOD are similar.
Angle ВOС = AOD as vertical angles at the intersection of the AC and ВD diagonals.
The angle OBC = ODA as criss-crossing angles at the intersection of parallel straight lines BC and BP of the secant HP.
Then the triangles ВOС and AOD are similar in two angles, the first sign of similarity of triangles.
Let us determine the coefficient of similarity of the triangles ВOС and AOD. K = BC / BP = 3/6 = 1/2.
Then OC / OA = 1/2.
OС = OA / 2 = 4/2 = 2 m.
Answer: The length of the OS segment is 2 m.