Timeless Theorems of Mathematics/Brahmagupta Theorem

The Brahmagupta's theorem states that if a cyclic quadrilateral is orthodiagonal (that is, has perpendicular diagonals), then the perpendicular to a side from the point of intersection of the diagonals always bisects the opposite side.Michael John Bradley (2006). The Birth of Mathematics: Ancient Times to 1300. Publisher Infobase Publishing. . Page 70, 85. The theorem is named after the Indian mathematician Brahmagupta (598-668). Proof Statement If any cyclic quadrilateral has perpendicular diagonals, then the perpendicular to a side from the point of intersection of the diagonals always bisects the opposite side. Proof thumb|If and then according to the Brahmagupta's theorem Proposition: Let is a quadrilateral inscribed in a circle with perpendicular diagonals and intersecting at point . is a perpendicular on the side from the point and extended intersects the opposite side at point . It is to be proved that . Proof: [As both are inscribed angles that intercept the same arc of a circle] Or, Here, ° Or, ° Again, ° Or, ° [As ° and ] Or, ° ° Or, Or, [As, \angle AMF = \angle CME; Vertical Angles] Therefore, In the similar way, and Or, [Proved] Reference