(adsbygoogle = window.adsbygoogle || []).push({}); 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.

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# Homework Help: Points that are symmetric with respect to a circle C

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