Brokard's theorem

Brokard's theorem (also known as Brocard's theorem) is a theorem in projective geometry. It is commonly used in Olympiad mathematics. It is named after French mathematician Henri Brocard.

An equivalent formulation of Brokard's theorem states that the orthocenter of the diagonal triangle of a cyclic quadrilateral is the circumcenter of the cyclic quadrilateral.

• Orthocenter
• Power of a point
• Pole and polar

• A proof without words of Brokard's theorem