n=3
Proof
Let
and
Phitagoras' theorem for
we construct - angle bisector
and (- tangent)
- exterior angle
-angle bisector
and - angle bisector
and and - chords
In conclusion it can be said that or
Poncelet's closure theorem for n=3
Note:
It also follows from the Euler's theorem: the distance between the cirdumcentre and incentre of a triangle is given by or equivalently .