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Notes on an orthocentric triangle

Published online by Cambridge University Press:  20 January 2009

R. Tucker
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1. In the accompanying figure DEF is the pedal triangle of ABC and P, Q, R are the orthocentres of AFE, BDF, CED.

AP, BQ, CR evidently meet in the circumcentre, O, of ABC, which is the orthocentre of PQR,

2. Now the circumradius of AFE(ρa) = RcosA,

hence the sides of PQR are equal and parallel to the sides of DEF, i.e., the triangles are congruent, and their centre of perspective, L, bisects DP, EQ, FR.

Type
Research Article
Information
Proceedings of the Edinburgh Mathematical Society , Volume 12 , February 1893 , pp. 118 - 119
Copyright
Copyright © Edinburgh Mathematical Society 1893

References

* See Proccedings, London Mathematical Society, Vol. xv., Appendix.)