Problem

Source: Czech and Slovak Olympiad 2019, National Round, Problem 2

Tags: constructive geometry, rectangle, geometry, national olympiad



Let be $ABCD$ a rectangle with $|AB|=a\ge b=|BC|$. Find points $P,Q$ on the line $BD$ such that $|AP|=|PQ|=|QC|$. Discuss the solvability with respect to the lengths $a,b$.