- #1

zhandele

- 7

- 0

## Homework Statement

Given the unit circle (in the Euclidean plane) centered at the origin x^2+y^2=1, and a general circle D with equation (x-a)^2+(y-b)^2=c^2 that does not pass through the origin (ie the center of inversion, ie a^2+b^2≠c^2, prove

**analytically**that the inversion of D in the unit cirlce is still a circle.

## Homework Equations

See the attached pdf files

## The Attempt at a Solution

I can prove this synthetically. I even worked out the equation of the image circle D', but I can't derive it algebraically. I feel I must be missing something very obvious.

I uploaded two pdf files. I was going to upload a GSP file, but I guess this forum can't do that? I'll have to generate pdfs from it or something. Do most of you guys have GSP? It's mind-bogglingly useful.