MathDB
isosceles trapezoid construction given 3 semgents, equal inradii

Source: 2017 XX All-Ukrainian Tournament of Young Mathematicians named after M. Y. Yadrenko, Qualifying p1

May 6, 2021
geometrytrapezoidisoscelesconstructionUkrainian TYM

Problem Statement

In an isosceles trapezoid ABCDABCD with bases ADAD and BCBC, diagonals intersect at point PP, and lines ABAB and CDCD intersect at point QQ. O1O_1 and O2O_2 are the centers of the circles circumscribed around the triangles ABPABP and CDPCDP, rr is the radius of these circles. Construct the trapezoid ABCD given the segments O1O2O_1O_2, PQPQ and radius rr.