Let $∆\mathrm{ABC}$ be any triangle and D, E, F feet of perpendicular from vertices A, B, C on opposite side BC, CA, AB, respectively. Then, the $∆\mathrm{DEF}$ is know as pedal A of ABC.
H is ortho centre of the $∆\mathrm{ABC}$. We note that $\mathrm{\angle }\mathrm{HDC}=\mathrm{\angle }\mathrm{HEC}={90}^{\circ }$, so the points H, D, C and E are concyclic.
In question AABC is assumed an acute angled triangle. In case AABC be obtuse angled with A as obtuse angle. The angle of pedal $∆$ will be 2A - 180°, 2B, 2C and side will be represented by - a cos A, b cos B, c cos C.