Points $A, B, C, D$ lie on a line $l$, in that order. Find the locus of points $P$ in the plane for which $\angle{APB}=\angle{CPD}$.
Problem
Source: 12-th Hungary-Israel Binational Mathematical Competition 2001
Tags: geometry proposed, geometry
Source: 12-th Hungary-Israel Binational Mathematical Competition 2001
Tags: geometry proposed, geometry
Points $A, B, C, D$ lie on a line $l$, in that order. Find the locus of points $P$ in the plane for which $\angle{APB}=\angle{CPD}$.