MathDB

1

Part of 1999 Korea Junior Math Olympiad

Problems(1)

Proving ABCD inscribed(only with strange conditions)

Source: 1999 KJMO

6/30/2024
There exists point OO inside a convex quadrilateral ABCDABCD satisfying OA=OBOA=OB and OC=ODOC=OD, and ∠AOB=∠COD=90∘\angle AOB = \angle COD=90^{\circ}. Consider two squares, (1)square having ACAC as one side and located in the opposite side of BB and (2)square having BDBD as one side and located in the opposite side of EE. If the common part of these two squares is also a square, prove that ABCDABCD is an inscribed quadrilateral.
geometryconvex quadrilateralinscribed quadrilateralKJMO