Show that in any triangle $ABC$ with $\angle A = 90^o$ the following inequality holds $$(AB -AC)^2(BC^2 + 4AB \cdot AC)^ 2 < 2BC^6.$$
Problem
Source: 2010 Saudi Arabia BMO TST 2.2 - Balkan
Tags: right triangle, geometry, geometric inequality
Source: 2010 Saudi Arabia BMO TST 2.2 - Balkan
Tags: right triangle, geometry, geometric inequality
Show that in any triangle $ABC$ with $\angle A = 90^o$ the following inequality holds $$(AB -AC)^2(BC^2 + 4AB \cdot AC)^ 2 < 2BC^6.$$