Three equilateral triangles and two line segments. Prove that the three red points are collinear.
Scroll down for a solution to this problem.
From congruence of triangles CAF and DAB and the fact that ∠DAC is 60° it follows that ∠DGC is 60°. Therefore quadrilateral DAGC is cyclic and so is AFBG. The intersection G is therefore the common point of the three circumcircles of the equilateral triangles.
Now its is seen that the three angles left from G add up to 180° and therefore it is a straight line.
Napoléon Bonaparte was not only
A military leader
Also a lover of mathematics
And strategic plans
He used the compas
For geometric figures
He liked scientific questions
As well as military instructions
And practical details
He left an immense scientific and political legacy