MathNet 2022-part-01 — 197 problems (EN–VI) Question 149

For a triangle $ABC$ it is known that $AB = c$, $BC = a$, $AC = b$ and $\angle BAC = 80^\circ$. Point $M$ on the side $AB$ is such that $\angle AMC = 70^\circ$. If $AM + AC = BC$, prove that $a^2 = b(b+c)$.