# 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.^{[1]}

The theorem is named after the Indian mathematician Brahmagupta (598-668).

## ProofEdit

### StatementEdit

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.

### ProofEdit

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 .

## ReferenceEdit

- ↑ Michael John Bradley (2006). The Birth of Mathematics: Ancient Times to 1300. Publisher Infobase Publishing. ISBN 0816054231. Page 70, 85.