Which triangle center is it?

Geometry Level 4

$AB=AD=BG \text{, } AC=AH=CF \text{, } BC=BI=CE$ .

$L$ is a midpoint of $ED$ , $K$ is a midpoint of $FG$ , $J$ is a midpoint of $HI$ .

What is point $P$ in $\triangle ABC$ ?

Circumcentre Centroid Incentre Fermat Point Nagel Point

1 solution

Maria Kozlowska
Jul 20, 2015

Nagel point is a point of intersecction of splitters. Splitters bisect perimeter of a triangle. Splitters ends are touch points of the excircles.