Simson’s line

Let $ABC$ a triangle and $P$ a point on its circumcircle (other than $A,B,C$).Then the feet of the perpendiculars drawn from P to the sides $AB,BC,CA$ (or their prolongations) are collinear.

In the picture, the line passing through $U,V,W$ is a Simson line for $\mathrm{△}ABC$.

An interesting result form the realm of analytic geometry states that the envelope formed by Simson’s lines when P varies is a circular hypocycloid of three points.