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construct point P such <APB= <BPC= <CPD iff (a+b)(b+c) < 4ac

Source: Austrian-Polish 1994

May 23, 2019
geometryequal anglesconstruction

Problem Statement

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