AUSTRIAN-POLISH 1994 Problem 9

On the plane are given four distinct points $A,B,C,D$ on a line $g$ in this order, at the mutual distances $AB = a, BC = b, CD = c$ . (a) Construct (if possible) a point $P$ outside line $g$ such that $\angle APB =\angle BPC =\angle CPD$ . (b) Prove that such a point $P$ exists if and only if $(a+b)(b+c) < 4ac$