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point construction M on line r such that <(r,AM)=2<(r,BM) fixed points A,B

Source: Spanish Mathematical Olympiad 1975 P5

December 23, 2022

geometryequal anglesconstruction

Problem Statement

In the plane we have a line

r

and two points

A

and

B

outside the line and in the same half plane. Determine a point

M

on the line such that the angle of

r

with

AM

is double that of

r

with

BM

. (Consider the smaller angle of two lines of the angles they form).