The bases of a trapezoid are equal to 144 and 145 Find the largest of the line segments into which

The bases of a trapezoid are equal to 144 and 145 Find the largest of the line segments into which one of its diagonals divides the middle line of this trapezoid.

Given:
AВСK – trapezoid,
ЕН – middle line,
ВС and AK – bases,
BC = 144,
AK = 145,
point O — the point of intersection of the AC diagonal and the EH midline.
Find the largest of the segments EO or OH -?
Decision:
EH is the midline of the ABC trapezoid, then EO is the midline of the ABC triangle, and the OH segment is the midline of the ACK triangle. Knowing that the middle line is equal to half of the side of the triangle, which is parallel.
Then EO = 1/2 BC;
EO = 1/2 * 144;
EO = (1 * 144) / 2;
EO = 72.
Then OH = 1/2 AK;
OH = 1/2 * 145;
OH = (1 * 145) / 2;
OH = 72.5.
Answer: OH = 72.5.