circles tangent to a fixed circle (2019 Novosibirsk Oral Geo Oly 8.6)
Source:
April 28, 2021
geometryfixedtangent circles
Problem Statement
Point is located in this circle of radius . An arbitrary chord is drawn through it, and then a circle of radius is drawn through the ends of this chord. Prove that all such circles touch some fixed circle, not depending from the initial choice of the chord.