# data[].attributes.body
Problem 11. If ABCD is a trapezoid with bases AB and CD, then: The line segment through the intersection of its diagonal

s and parallel to its bases is the harmonic mean of the bases;

The line segment joining the midpoints of the legs of the trapezoid is the arithmetic mean of the bases;

The line that divides the trapezoid into two similar trapezoids (and is parallel to the bases) is the geometric mean of the bases.

Problem 12. If P is a point on diameter AB of circle (O) then (see figure) :

ZY is the harmonic mean of AP and PB;

OX is the arithmetic mean of AP and PB;

PY is the geometric mean of AP and PB.

Problem 13: In the figure, AC||EF||BD. Show that 1/EF=1/AC +1/BD