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On a Chain of Circle Theorems
Published online by Cambridge University Press: 31 October 2008
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If P1, P2, P3, P4 are four points on a circle C, and P234 is the orthocentre of triangle P2 P3 P4, P134 the orthocentre of triangle P1 P3 P4 and so on, then the quadrilateral P234 P134 P124 P123 is congruent to the quadrilateral P1 P2 P3 P4. This theorem seems to be due to Steiner (Ges. Werke, 1, p. 128; see H. F. Baker, Introduction to Plane Geometry, 1943, p. 332) and has appeared frequently since in collections of riders on the elementary circle theorems.
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- Copyright © Edinburgh Mathematical Society 1944
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