circumscribed quadrilateral [OA*OC + OB*OD = sqrt(abcd)]
Source: Chinese TST 2003
September 20, 2005
geometrytrigonometrycalculusgeometry proposed
Problem Statement
Let be a quadrilateral which has an incircle centered at . Prove that
OA\cdot OC\plus{}OB\cdot OD\equal{}\sqrt{AB\cdot BC\cdot CD\cdot DA}