MathDB

2

Part of 2015 İberoAmerican

Problems(1)

An angle bisector cuts a line at a point with a property

Source: 2015 Iberoamerican Olympiad. Problem 2

11/10/2015
A line rr contains the points AA, BB, CC, DD in that order. Let PP be a point not in rr such that ∠APB=∠CPD\angle{APB} = \angle{CPD}. Prove that the angle bisector of ∠APD\angle{APD} intersects the line rr at a point GG such that:
1GA+1GC=1GB+1GD\frac{1}{GA} + \frac{1}{GC} = \frac{1}{GB} + \frac{1}{GD}
geometryangle bisectorInversion