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Two Another Powerian Pairs In Arbelos

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  • Quang Tuan Bui
    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
    Message 1 of 1 , Jul 30, 2008
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      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.

      Best regards,
      Bui Quang Tuan
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