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. 

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.