ABCD rhombus. The diagonals of which intersect at point O. Segment ОF is the median of triangle AOB.

ABCD rhombus. The diagonals of which intersect at point O. Segment ОF is the median of triangle AOB. Calculate the length of the AC diagonal. If ОF is 3 cm and the length of the segment АС is more than the length ВС by 4 cm.

Consider a right-angled triangle AOB, whose angle O = 90, and OE, by condition, is the median of the triangle.

By the property of a right-angled triangle, the length of the median drawn at the hypotenuse of a triangle is equal to half the length of the hypotenuse.

Then ОF = AB / 2.

AB = 2 * OF = 2 * 3 = 6 cm.

Since all sides of a rhombus are equal, BC = AB = 6 cm.

AC is more than BC, by condition, by 4 cm, then AC = AB + 4 = 6 + 4 = 10 cm.

Answer: The length of the AC diagonal = 10 cm.