MathNet 2019-part-02 — 184 problems (EN–VI) Question 131

Point $T$ is located inside the triangle $ABC$ so that $|AT| = 56$, $|BT| = 40$ and $|CT| = 35$. The feet of the altitudes from $T$ to the sides of $ABC$ are vertices of an equilateral triangle. Find $\triangle ABC$.

(Belarus 2018)