22069Homothetic Center - Locus
- Mar 25, 2014APHA'B'C', (L1,L2,L3) or (M1,M2,M3) parallelogic?ABC, (L1,L2,L3) or (M1,M2,M3) are parallelogic?Which is the locus of P such that:Loci:Homothetic center ? (in terms of the hom. coordinates of P)The triangles bounded by (L1,L2,L3) and (M1,M2,M3) are homothetic.Similarly L2, M2 and L3, M3L1 and M1 are parallel (since both are perpendicular to AbAc)M1 = the radical axis of the circle (Ab, AbC') and (Ac, AcB')L1 = the radical axis of the circles (Ab, AbB') and (Ac, AcC')Ab, Ac = the orthogonal projections of A' on PB',PC', resp.Denote:Let ABC be a triangle, P a point and A'B'C' the pedal triangle of P.
(I think H is on both loci.)