An elementary treatise on modern pure geometry (1893)
Lachlan, Robert · London, New York, Macmillan and Co. · leaf 88
ABC are proportional toKX, KY, KZ; and therefore they are proportional to the sides of the triangleABC. The Nine-Point circle. 123. If 8 be the circumcentre, and 0 the orthocentre, of thetriangle ABC; B,E,F the middle points of the sides; P, Q, R OF A TRIANGLE. 71 the feet of the perpendiculars… … Since S and 0 are isogonal conjugate points with respect tothe triangle ABC, it follows that a circle can be drawn throughthe points P, Q, R, B, E, F (§ 102, Ex. 2). Again, since A is theorthocentre of the triangle BOO (^ H-i), it follows that the pointsP, Q, R, Y, Z, D lie on the same circle.…
Geometry
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