A the (first, or internal) Kenmotu point, also called the congruent squares point, is the triangle center constructed by inscribing
three equal squares such that each square touches two sides and all three squares
touch at a single common point. The Kenmotu point is Kimberling
center 
and has equivalent triangle center functions
 |  |  |
(1)
|
 |  |  |
(2)
|
It was first found by J. Rigby (Kimberling 1998, p. 268).
The contact points of the squares with the sides are concyclic and lie on the Kenmotu circle, which has radius
equal to 
times the square edge length.
The definition in terms of inscribed squares breaks down for certain classes of triangles, at which point the vertices opposite the Kenmotu point can lie outside the triangle
and the isosceles
right triangles that remain in the interior of the triangle can overlap one another.
This happens when the Kenmotu circle becomes tangent
to a side.
The edge lengths of the inscribed squares are
 |
(3)
|
where 
is the area of the reference triangle 
(Kimberling 1998, p. 268).
The Kenmotu point lines on the Brocard axis.
Its isogonal conjugate is the inner Vecten point 
,
and is the perspector of a number of pairs of named
triangles.
The "free" vertices of the squares are perspective to the reference triangle at 
,
which could be considered the second, or external, Kenmotu point.
