I recently found this problem in my maths book, and I don't know how I should solve it:

*Show that $\displaystyle L^2=(ab+cd)(ac+bd)/(bc+ad)$*
I looked in the answers section of the book, and there it said that I should begin by using the law of cosines on the triangles ABD and BDC, and then use the fact that $\displaystyle \cos C= -\cos A$, as $\displaystyle A+C=180$ degrees. Why is that? Have I forgotten about some basic geometric rule or something?

opposite angles of a quadrilateral inscribed in a circle are supplementary.