Sharygin 2019, correspondence round, problem 5
Sharygin 2019, correspondence round, problem 5 is a plane geometry problem from the Sharygin Geometry Olympiad 2019, correspondence round, problem 5 (grades 8–9): the locus of the second common point of two circles.
Problem
Let $A$, $B$, $C$ and $D$ be four points in general position, and $\omega$ be a circle passing through $B$ and $C$. A point $P$ moves along $\omega$. Let $Q$ be the common point of circles $ABP$ and $PCD$ distinct from $P$. Find the locus of points $Q$.
Source Sharygin Geometry Olympiad 2019, correspondence round, problem 5 (grades 8–9)
The diagram
Drag any point and the whole construction follows; ▶ runs a point along its path and back. Tap a point to pin it, double-click to go back to the start. Effects redraws the figure in grayscale for print, in colour, or with the givens in focus.