MathDB

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

Source: 2015 Iberoamerican Olympiad. Problem 2

November 10, 2015

geometryangle bisectorInversion

Problem Statement

A line

r

contains the points

A

B

C

D

in that order. Let

P

be a point not in

r

such that

\angle{APB} = \angle{CPD}

. Prove that the angle bisector of

\angle{APD}

intersects the line

r

at a point

G

such that:

\frac{1}{GA} + \frac{1}{GC} = \frac{1}{GB} + \frac{1}{GD}