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| | no-pp = true}}</ref> It is commonly used in ]. | | no-pp = true}}</ref> It is commonly used in ]. | ||
Revision as of 18:49, 26 December 2024
Theorem about orthocenter and polars in circle geometryBrokard's theorem is a theorem in projective geometry. It is commonly used in Olympiad mathematics.
Statement
Brokard's theorem. The points A, B, C, and D lie in this order on a circle with center O'. Lines AC and BD intersect at P, AB and DC intersect at Q, and AD and BC intersect at R. Then O is the orthocenter of . Furthermore, QR is the polar of P, PQ is the polar of R, and PR is the polar of Q with respect to .
with center O'. Lines AC and BD intersect at P, AB and DC intersect at Q, and AD and BC intersect at R. Then O is the orthocenter of 
. Furthermore, QR is the See also
- Coxeter, H. S. M. (1987). Projective Geometry (2nd ed.). Springer-Verlag. ISBN 0-387-96532-7.
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