   ###### Online Geometry Problem 871: Brahmagupta's Theorem, Cyclic Quadrilateral, Perpendicular Diagonals, Midpoint. Level: High School, College, Mathematics Education

Brahmagupta's theorem states that if a cyclic quadrilateral ABCD has perpendicular diagonals, then the perpendicular to a side from the point of intersection of the diagonals always bisects the opposite side. Brahmagupta (598–668) was an Indian mathematician and astronomer who discovered a neat formula for the area of a cyclic quadrilateral.

See also: Corollary, Area Formula, Area Formula Extension, .

Geometry problem solving is one of the most challenging skills for students to learn. When a problem requires auxiliary construction, the difficulty of the problem increases drastically, perhaps because deciding which construction to make is an ill-structured problem. By “construction,” we mean adding geometric figures (points, lines, planes) to a problem figure that wasn’t mentioned as "given."

 Home | Search | Geometry | Problems | All Problems | Open Problems | Visual Index | 871-880 | Cyclic quadrilateral with perpendicular diagonals | Brahmagupta | Classical Theorems | Midpoint | Email | Solution / comment | By Antonio Gutierrez  