An elementary treatise on modern pure geometry (1893)
Lachlan, Robert · London, New York, Macmillan and Co. · leaf 163
D, E, F be the middle points of the sides of the triangleABC; and A, B, C the middle points of AO, BO, CO, where 0is the orthocentre. Then the perpendiculars at the middle points of AB,AB, ARare corresponding lines. But these lines meet in the point F. Similarly, the perpendiculars at the middle… … Hence, by § 225, D, E, F are points on the circle of similitude ;that is, the circle ABC Again, the perpendiculars at the middle points of BC, AC, A Bmeet in A. Therefore A is one of the invariable points of thesjstem. Similarly B, C are the other invariable points. HenceA, B, C lie on the circle…
Geometry
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