Spieker center
The Spieker center is defined as the center of mass of the perimeter of the triangle. The Spieker center of a is the center of gravity of a homogeneous wire frame in the shape of
The Spieker center is a triangle center and it is listed as the point
Incenter of medial triangle
Prove that is the incenter of the medial triangle
of a
Proof
Let's hang up the in the middle of side
Side
is balanced.
Let's replace side with point
(the center of mass of
the midpoint
Denote
the linear density of a homogeneous wire frame.
The mass of point is equal to
the shoulder of the gravity force is
The moment of this force is
Similarly the moment gravity force acting on AB is
Therefore, equilibrium condition is and the center of gravity of a homogeneous wire frame
lies on each bisector of
This point is the incenter of the medial triangle
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