Brokard's theorem

Brokard's theorem (also known as Brocard's theorem) is a theorem on poles and polars in projective geometry commonly used in Olympiad mathematics. 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 .Heuristic ID Team (2021), HEURISTIC: For Mathematical Olympiad Approach 2nd Edition, p. 99. (in Indonesian)

See also Orthocenter Power of a point Pole and polar

References

External links Proof of Brokard's theorem A proof without words of Brokard's theorem