MathDB
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 ABCDABCD with bases ADAD and BCBC is inscribed in a circle, MM is the intersection of of its diagonals. A straight line passing through MM perpendicular to the bases intersects BCBC at pointK K, and the circle at point LL, where LL is the one of the two intersection points for which MM lies on the segment KLKL. It is known that MK=aMK = a, LM=bLM = b. Find the radius of the circle tangent to the segments AMAM, BMBM and the circle circumscribed around ABCDABCD.