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

univerkov | March 27, 2021 | education

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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