intersecting at a point P. Then every tangent

points {Q,R} and the conic at two points {S,T} of which one, S say, is the

The proof starts by defining the polar FE of P with respect to the conic

circle

consider the intersection point A of CB with the polar EF. The polar

reciprocity of relation pole-polar) and is parallel to tangent

lines at P: P(E,F,J,A) defines a harmonic division on every line it meets. Apply this to the tangent

tangent, S is the harmonic conjugate with respect to {R,Q} of the point at infinity of line

S of segments RQ intercepted by tangents

the given lines {

The proof of this inverse can be easily supplied by constructing the hyperbola from the given data and then using its proven property

identify it with the required locus. A similar property defining hyperbolas is discussed in HyperbolaProperty.html .

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