Data Sufficiency

The only way both statements can be true together is if R, P and Q are not points on the circle. We can certainly have a tangent line PR that touches the circle at a different point- A, say, and QR might touch the circle at B. Once you see this, it quickly becomes clear that neither statement is sufficient on its own. When you consider both statements together, there is a lot of work involved, unless I'm missing a trick. If POR is isosceles, we need to consider three possibilities- PO = PR, PO = OR and PR = OR- and we need to do the same for the other isosceles triangle. It's far too much work for a GMAT question, and I'm wondering if additional information was provided in the question (a diagram, perhaps?). Also curious about where the question is from.