Waste less time on Facebook — follow Brilliant.

Lemoine Circle and Isogonality

Prove that the First Lemoine Circle has Brocard midpoint (the center of Brocard circle) as a center.

See First Lemoine circle and Brocard circle.

My first wild guess was that First Lemoine Circle has centroid as a center, because Lemoine point is isogonal conjugate to centroid. But it turns out wrong. Why?!

From the theorem of Second Lemoine Circle we know that Second Lemoine Circle has a center exactly at Lemoine Point. Isogonality, the center of First Lemoine Circle should be at centroid, isn't it?

Note by Samuraiwarm Tsunayoshi
2 years, 4 months ago

No vote yet
1 vote


There are no comments in this discussion.


Problem Loading...

Note Loading...

Set Loading...