Problem

Source: 10.2 Final Round of Sharygin geometry Olympiad 2013

Tags: inequalities, geometry proposed, geometry



Let $ABCD$ is a tangential quadrilateral such that $AB=CD>BC$. $AC$ meets $BD$ at $L$. Prove that $\widehat{ALB}$ is acute.

HIDE: Click to reveal hidden text According to the jury, they want to propose a more generalized problem is to prove $(AB-CD)^2 < (AD-BC)^2$, but this problem has appeared some time ago