This is just a question I have been thinking about for a few days. Let's say we have a right triangle with vertices at (0,0), (a,0) and (a,b). Now, consider that an arc has been constructed with centre (x,y) and that the arc passes through the vertices (0,0) and (a,b) so the arc is 'over' the hypotenuse. What is the locus of points of the centre of the arc? Geometrically, does the centre of the arc lie on a circle/ellipse or something else?
I hope this question has made some sense - please comment if you require any further explanation!