computational with inscribed trapezoid
Source: II Soros Olympiad 1995-96 R3 10.9 https://artofproblemsolving.com/community/c2416727_soros_olympiad_in_mathematics
June 6, 2024
geometrytrapezoid
Problem Statement
Trapezoid with bases and is inscribed in a circle, is the intersection of of its diagonals. A straight line passing through perpendicular to the bases intersects at point, and the circle at point , where is the one of the two intersection points for which lies on the segment . It is known that , . Find the radius of the circle tangent to the segments , and the circle circumscribed around .