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

August 28, 2021 | education

| **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.

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