Brocard Points of the Triangle

Given three points A, B and C,
find the point P such that angle(PAB) = angle(PBC) = angle(PCA).
Express tan(PAB) in terms of A, B and C.
introduction
construction of P
calculation of tan(PAB)
the other point P
coordinates of P

(applet)
java applet or image[Java applet]

O is such that angle(OAC) = angle(OCB) = angle(OBA)

O is also the isogonal conjugate of P: if PA, PB and PC are mirrored across the angle bisectors, their images concur at O.