Brahmagupta Theorem

Theorem
Let $$ABCD$$ be the tetragon, which can be inscribed to some circle $$k$$, such that lines $$AC$$ and $$BD$$ are perpendicular. Call the intersection of these two lines $$E$$. Let $$F$$ is some point, which belongs to segment $$AB$$. Line $$EF$$ is perpedicular to $$CD$$ if and only if $$F$$ is midpoint of segment $$AB$$.

Proof

 * [[Image:Brahmagupta.PNG]]