Basic Math Problem of the Week 9/21/2017

[PF PotW Robot]

Here is this week's basic math problem. We have several members who will check solutions, but we also welcome the community in general to step in. We also encourage finding different methods to the solution. If one has been found, see if there is another way. Using spoiler tags is optional. Occasionally there will be prizes for extraordinary or clever methods.

The sum of the angles $A$ and $C$ of a convex quadrilateral $ABCD$ is less than $180^\circ$.

Prove that $AB\cdot CD+AD \cdot BC <AC(AB+AD)$

(PotW thanks to our friends at http://www.mathhelpboards.com/)

 

[fresh_42]

Hint: Ptolemy's theorem and Ptolemy's inequality.