Brokard's theorem
Theorem about orthocenter and polars in circle geometry
From Wikipedia, the free encyclopedia
Brokard's theorem (also known as Brocard's theorem[1]) is a theorem on poles and polars in projective geometry commonly used in Olympiad mathematics.[1][2][3] It is named after French mathematician Henri Brocard.
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 .[1][4][5]
