Problems(1)
Let ABC be an acute-angled triangle with AB<AC, and let O,H be its circumcentre and orthocentre respectively. Points Z,Y lie on segments AB,AC respectively, such that ∠ZOB=∠YOC=90∘. The perpendicular line from H to line YZ meets lines BO and CO at Q,R respectively. Let the tangents to the circumcircle of △AYZ at points Y and Z meet at point T. Prove that Q,R,O,T are concyclic. Proposed by Kazi Aryan Amin and K.V. Sudharshan geometry