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 illstructured problem. By
“construction,” we mean adding geometric figures (points, lines,
planes) to a problem figure that wasn’t mentioned as "given."
