Problem 1779 (difficulty: 5/10)

Let \(\displaystyle C\) be a circle, and \(\displaystyle p\) a point outside of \(\displaystyle C\). Show that if \(\displaystyle f\) is a fractional linear transformation such that \(\displaystyle f(C)=C\) and \(\displaystyle f(p)=p\), then \(\displaystyle |f'(p)|=1\).

Give me another random problem!

Subject, section:
Requested difficulty:
Request for a concrete problem:I want problem no.

Supported by the Higher Education Restructuring Fund allocated to ELTE by the Hungarian Government