Question

ABCD is a rectangle. The line through C perpendicular to AC meets AB produced at X and AD produced at Y .Prove that D,B,X,Y are concyclic.

Answer 1

If you refer to the diagram you can find that side AC is perpendicular to side xy and side CD is perpendicular to side BC not only this but also angle oh is 90 degree and Angle DC why is 90 degree because summing angle dyc and Y is equal to 90 degree. To prove the sides are concyclic if we can make sure the opposite angles are supplementary that is something the angles will be equal to 180 then it can be proved easily