8. Brahmagupta’s Theorem - Deepstash
8. Brahmagupta’s Theorem

8. Brahmagupta’s Theorem

Brahmagupta theorem states that,

If a cyclic quadrilateral is orthodiagonal (i.e., has perpendicular diagonals), then the perpendicular to a side from the point of intersection of the diagonals always bisects the opposite side.”

Geometrically, this theorem means that, in a cyclic quadrilateral ABCD, diagonals AC and BD are perpendicular to each other. The intersection of AC and BD is M. Drop the perpendicular from M to the line BC, calling the intersection point E. Let F be the intersection of the line EM and the side AD. Then, according to the theorem, F is the midpoint of side AD.

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