13.0 Orthocentre and Pedal Triangle

The triangle which is formed by joining the feet of the altitudes is called pedal triangle. As shown in figure,

triangle $PQR$ is a pedal triangle.

Angles of pedal triangle are $$\pi - 2A,\pi - 2B,\pi - 2C$$

Sides are given as $$\begin{equation} \begin{aligned} a\cos A = 2R\sin 2A \\ b\cos B = 2R\sin 2B \\ c\cos C = 2R\sin 2C \\\end{aligned} \end{equation} $$

Circumradii of triangle $HBC$, $HCA$, $HAB$ and $ABC$ are equal where $H$ is the orthocentre of the triangle.