Let's construct a symmetric trapezoid, given the length of the non-parallel sides $(c)$, the length of the diagonal $(d)$, and the angle between the diagonals!

Let's examine the possibility of construction, especially in the case when the angle opposite the non-parallel sides is $60^{\circ}$.
I. Solution. Let $ABCD$ be the sought trapezoid and $ABc$, so that the trapezoid is convex.

If $\alpha=60^{\circ}$, then $c$ is equal to the side of the regular hexagon inscribed in the circle; the diameter of the circle is $2c$ and the condition for the possibility of the construction is

$$
c<d<2c
$$

the same as under I.


[^0]:    ${ }^{1}$ If it is a convex trapezoid, then $c<d$!