1. The problem statement, all variables and given/known data Lemma 1: Fix the circle C with center (x nought, y nought); y nought is greater than 0 and radius R is less than y nought. Consider two points P (x nought, y noight tilde) and P prime (x nought, -y nought tilde) which are symmetric with respect to x-axis by construcion. Prove that P and P prime are also symmetric with respect to Circle C if and only if y nought tilde is equal to the sqrt (y nought squared - radius squared). 2. Relevant equations on the attachment 3. The attempt at a solution I believe that these two points are orthogonal with respect to the x-axis. and they are symmetric because they fall on the same ray.