four circles , tangencies
Source: III Soros Olympiad 1996-97 R2 11.4 https://artofproblemsolving.com/community/c2416727_soros_olympiad_in_mathematics
May 31, 2024
geometrycirclestangent circles
Problem Statement
There are four circles. The chord is drawn in the first one, and the distance from the midpoint of the smaller of the two formed arcs to is equal to . The second, third and fourth circles are located inside the larger segment and touch the chord . The second and fourth circles touch internally the first and externally the third. The sum of the radii of the last three circles is equal to the radius of the first circle. Find the radius of the third circle if it is known that the line passing through the centers of the first and third circles is not parallel to the line passing through the centers of the other two circles.