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If in a triangle ABC, points are taken on the sides such that
then the radical axis of the circles PQR, P′Q′R′ passes through the centroid and “S.” points of ABC; and if QR, Q′R′ cut in 1, RP, R′P′ in 2, PQ, P′Q′ in 3, then the equation to the circle 123 is
* (20)Rev. W. A. Whitworth in Mathematical Questions from the Educational Times, X. 51 (1868).