The bisectors of the angles of the trapezoid, adjacent to the lateral side AB, intersect at point o.

univerkov | January 1, 2021 | education

The bisectors of the angles of the trapezoid, adjacent to the lateral side AB, intersect at point o. find the distance from point o to the middle of the segment AB, if AB is 8 cm.

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 triangle AOB is rectangular. Point M is the middle of side AB, then the segment OM is the median of a right-angled triangle drawn from a right angle to the hypotenuse, which means it is equal to half the length of the hypotenuse.
OM = AB / 2 = 8/2 = 4 cm.
Answer: The distance from point O to the middle of AB is 4 cm.

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