Miquel Triangle

Given a point $P$ and a triangle $\Delta A_1A_2A_3$, the Miquel triangle is the triangle connecting the side points $P_1$, $P_2$, and $P_3$ of $\Delta A_1A_2A_3$ with respect to which $P$ is the Miquel Point. All Miquel triangles of a given point $M$ are directly similar, and $M$ is the Similitude Center in every case.