How to draw an isosceles trapezoid with a given angle between diagonals?

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I have an isosceles trapezoid with an angle between diagonals $60^\circ$, the diagonal is $10$ cm and the legs are $6$ cm. Can you explain to me how to make the graph? Thank you in advance!

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(1) Draw $\triangle ABC$ such that $\angle BAC=120^\circ$ and $AB=AC=10$ cm.

(2) Through $A$ draw a line $\ell$ parallel to $BC$.

(3) Draw a circular arc centred at $C$ with radius $6$ cm, cutting $\ell$ at $D$. (There are two possible positions of $D$.)

(4) Through $D$ draw a line parallel to $AB$, cutting $BC$ at $E$.

$ADCE$ is the required isosceles trapezoid.