Let W,X,Y and Z be points on a circumference ω with center O, in that order, such that WY is perpendicular to XZ; T is their intersection. ABCD is the convex quadrilateral such that W,X,Y and Z are the tangency points of ω with segments AB,BC,CD and DA respectively. The perpendicular lines to OA and OB through A and B, respectively, intersect at P; the perpendicular lines to OB and OC through B and C, respectively, intersect at Q, and the perpendicular lines to OC and OD through C and D, respectively, intersect at R. O1 is the circumcenter of triangle PQR. Prove that T,O and O1 are collinear.Proposed by CDMX Mexicogeometrycyclic quadrilateraltangential quadrilateralcollinear