Online Geometry Problem 871: Brahmagupta's Theorem, Cyclic Quadrilateral, Perpendicular Diagonals, Midpoint. Level: High School,
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.
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."