Complete Quadrilateral
Complete quadrilateral
Let four lines made four triangles of a complete quadrilateral. In the diagram these are
One can see some of the properties of this configuration and their proof using the following links.
Radical axis
Let four lines made four triangles of a complete quadrilateral. In the diagram these are
Let points and
be the orthocenters of
and
respectively.
Let circles and
be the circles with diameters
and
respectively.
Prove that Steiner line
is the radical axis of
and
Proof
Let points and
be the foots of perpendiculars
and
respectively.
Denote power of point
with respect the circle
Therefore power of points
and
with respect these three circles are the same, these points lies on the common radical axis of
and
Steiner line
is the radical axis as desired.