Point $M$ lies inside an isosceles right $\triangle ABC$ with hypotenuse $AB$ such that $MA=5$, $MB=7$, $MC=4\sqrt{2}$. Find $\angle AMC$.
Source: Bulgarian Autumn Tournament 2022 12.2
Tags: geometry
Point $M$ lies inside an isosceles right $\triangle ABC$ with hypotenuse $AB$ such that $MA=5$, $MB=7$, $MC=4\sqrt{2}$. Find $\angle AMC$.