# 2018 January Challenge: Geometry [closed]

Considering it's the beginning of a new year, I have created the following challenge. I hope to make one every month until December 2018!

Here goes:

Show that $$AD-AB>AC^3$$. Do not use scale drawings.

Note that this post was advised to be migrated to Puzzling Stack Exchange from Mathematics.

• the diagram given seems sufficient to give precise lengths for every line segment, so the lengths can be resolved to surds and the inequality proven that way, – Jasen Jan 21 '18 at 1:37
• @Jasen are you assuming DC is parallel to the bottom segment? – boboquack Jan 22 '18 at 23:54
• @boboquack Yes. I was. Oops! – Jasen Jan 23 '18 at 5:26
• @boboquack but if it's not disproof is trivial. it sure looks like AD−AB can be made negative. – Jasen Jan 23 '18 at 5:33