I finished this proof that took about a whole page and I was just wondering if there were an easier way of doing things that would take less work. here's the problem. PQ and PR are two chords of a circle with centre O. OT is perpendicular to PQ and OS is perpendicular to PR. IF OT = OS prove that T,S,R and Q are concyclic. I am going to go through my steps without proof cause it would take forever. I just want to get an idea if I am doing it the easiest way. It would probably help if you drew this out. First I proved QT = RS then QTO is congruent to RSO Then you can prove TS is parallel to QR from there i can conclude that <QSR = <QTR from there can I conlude that they are concyclic by equal angles in a segment? Edit: I realized that I didn't need to prove parallel lines. It really doesn't help the question in any way.