Brahmagupta's theorem is a result in geometry. It states that if a cyclic quadrilateral has perpendicular diagonals, then the perpendicular to a side from the point of intersection of the diagonals always bisects the opposite side. It is named after the Indian mathematicianBrahmagupta. Geometry (Greek geo = earth, metro = measure) {put in greek letters here, check accuracy} arose as the field of knowledge dealing with spatial relationships. ... In geometry, a cyclic quadrilateral is a quadrilateral whose vertices all lie on a single circle. ... For the Deep Purple album, see Purpendicular. ... Here is a chronology of the main Indian mathematicians: BC Yajnavalkya, 1800 BC, the author of the altar mathematics of the Shatapatha Brahmana. ... Brahmagupta (ब्रह्मगुप्त) (598_668) was an Indian mathematician and astronomer. ...
Brahmagupta attempted at constructing a square of area equalling that of a circle by assuming that pi would converge at sqrt(10).
Some of the important contributions made by Brahmagupta in astronomy are: methods for calculations of the motions and places of various planets, their rising and setting, conjunctions, and the calculation of eclipses of the sun and the moon.
The theorem states that the sum of the distances from the circumcenter, O, to the three sides is equal to the sum of the radii of the incircle and the circumcircle.
The theorem states that in an equilateral triangle, the sum of the perpendicular distances to the sides is equal to the altitude of the triangle.
The theorem can be generalized to a regular n-gon to state, for any point P interior to a regular n-gon, the sum of the perpendicular distances to the n sides is n times the apothem of the figure.
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