MathDB

9.1

Part of 2005 Sharygin Geometry Olympiad

Problems(1)

perpendicular diagonals criterion for a cyclic quadrilateral

Source: Sharygin 2005 Finals 9.1

8/26/2019
The quadrangle ABCDABCD is inscribed in a circle whose center OO lies inside it. Prove that if ∠BAO=∠DAC\angle BAO = \angle DAC, then the diagonals of the quadrilateral are perpendicular.
cyclic quadrilateralequal anglesperpendiculardiagonalsgeometry