MathDB

2017.1

Part of Ukrainian TYM Qualifying - geometry

Problems(1)

isosceles trapezoid construction given 3 semgents, equal inradii

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

5/6/2021
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.
geometrytrapezoidisoscelesconstructionUkrainian TYM