5

Part of 1975 Spain Mathematical Olympiad

Problems(1)

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

Source: Spanish Mathematical Olympiad 1975 P5

In the plane we have a line

r

A

B

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

M

on the line such that the angle of

r

AM

is double that of

r

BM

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

geometryequal anglesconstruction