Bicentric2

Bicentric quadrilaterals

Bicentric quadrilaterals q = ABCD are these that have both circumcircle (b) and incircle (a). They have also a number of properties related to the two circles and the [Projective Collinearity] T of q. These were discussed in Bicentric.html .
Here I illustrate a feature connected with T. As shown in the previous reference, circles (a), (b) generate a (coaxal) circle bundle I(a,b) of non intersecting type. The member circles of this bundle are invariant under the projective collinearity T of the quadrangle q, which is identical with the projective collinearity T' of the quadrangle q'. The figure below shows the images via T of circles (k) of the orthogonal to I(a,b) circle bundle II. They are rectangular hyperbolas k* with center at S, which is the intersection point of the axes of the two bundles. k and its k* = T(k) are tangent at E, which is one of the limit points of bundle I(a,b).

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