Perimeter of a circumscribed trapezoid

Question

"Find the perimeter of the trapezoid:"

I know that if a trapezium is circumscribed, then it should satisfy Pitot theorem, but nothing else.

Also, found the height and length of one side, with the $30,60,90$º triangle that is created with the height of the trapezoid and that side.

Any hints?

Answer 1

Since you only wanted a hint, I drew a more detailed picture for you.v

BTW. A $53^\circ$-$37^\circ$-$90^\circ$ right triangle, is a $3$-$4$-$5$ right triangle with the angles rounded off to the nearest degree.

Answer 2

If $x$ is the distance from the $30°$ vertex to the tangency points nearest to it, then $x=2/\tan15°$. Similar formulas hold for the other vertices.