The bases of a trapezoid are equal to 4 and 10. Find the largest of the line segments into which

The bases of a trapezoid are equal to 4 and 10. Find the largest of the line segments into which one of its diagonals divides the middle line of this trapezoid.

Given:

trapezoid ABCE,
ВС and АЕ – bases,
BC = 4,
AE = 10,
OH – middle line,
AC – diagonal.
Find the largest of the segments into which the AC diagonal divides the middle line OH -?

Decision:
Consider a triangle ABC. The OE segment is its midline. We know that the middle line of a triangle is half the side to which it is parallel.
Therefore OE = 1/2 * BC;
OE = 1/2 * 4;
OE = (1 * 4) / 2;
OE = (1 * 2) / 1;
OE = 2.
Consider the ACE triangle.
EH = 1/2 * AE;
EH = (1 * 10) / 2;
EH = (1 * 5) / 1;
EH = 5.
Answer: 5.