MathNet 2021 — Part 04 Question 16

Let $ABC$ be a triangle with $\angle A\gt90^\circ$. Let $BE$ bisect $\angle ABC$, with $E\in AC$, and let $CF$ bisect $\angle ACB$, with $F\in AB$. Set $BE\cap CF=\{I\}$. Given that $IE=IF$, prove that $ABC$ is isosceles.