Two Another Powerian Pairs In Arbelos
- Dear All My Friends,
We use famous arbelos: C is one point on the segment AB; (O), (O1), (O2) are semicircles taken AB, AC, BC as diameters respectively. The perpendicular with AB from C intersects (O) at D. r1, r2 are radii of (O1), (O2) resp. Denote X(Y) as a circle centered at X passing through Y.
P1 = intersection of A(C) and B(D)
P2 = intersection of B(C) and A(D)
(We choose intersections in one side with semicircle (O) wrt AB)
It is easy to calculate P1O as a median of triangle P1AB and P2O as median of triangle P2AB and P1O^2 = P2O^2 = (r1^2 + r2^2). Therefore we can construct two Powerian pairs at P1, P2.
Bui Quang Tuan