consider a right angle moving rigidly so that one leg remains on the point "p" and the other leg is tangent to the curve. then the vertex of this angle is "x" and traces out the pedal curve. as the angle moves, its direction of motion at "p" is parallel to "px" and its direction of motion at "r" is parallel to the tangent "t" = "rx". therefore, the instant center of rotation is the intersection of the line perpendicular to "px" at "p" and perpendicular to "rx" at "r", and this point is "y". if follows that the tangent to the pedal at "x" is perpendicular to "xy".