ABCD is a trapezoid. BC and AD are foundations. O is the point of intersection of the diagonals. AO = 7.5 cm.

univerkov | August 1, 2021 | education

ABCD is a trapezoid. BC and AD are foundations. O is the point of intersection of the diagonals. AO = 7.5 cm. BO = 4 cm. OD = 5 cm. Find OC

The diagonals of the trapezoid divide the trapezoid into four triangles, two of which, at the bases of the trapezoid, are similar in two angles.

Let us determine the coefficient of similarity of the triangles BOC and AOD.

K = OВ / OD = 4/5.

Then OC / OA = 4/5.

OC / 7.5 = 4/5.

OC = 4 * 7.5 / 5 = 6 cm.

Answer: The length of the OC segment is 6 cm.

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