# The bisectors of the angles of the trapezoid, adjacent to the lateral side of CD, intersect at point O.

The bisectors of the angles of the trapezoid, adjacent to the lateral side of CD, intersect at point O. Find the distance from point O to the middle of the segment CD if CD = 12cm.

Since, by condition, the bisectors are drawn from the corners belonging to the lateral side, by their property they intersect at point O at a right angle and point O lies on the midline of the trapezoid.

Then the triangle COD is rectangular. Point K is the middle of the CD side, then the segment OK is the median of a right triangle drawn from a right angle to the hypotenuse, which means it is equal to half the length of the hypotenuse.

OK = CD / 2 = 12/2 = 6 cm.

Answer: The distance from point O to the middle of CD is 6 cm.

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