MathDB

5

Part of 2018 Czech and Slovak Olympiad III A

Problems(1)

Isosceles trapezoid

Source: Czech and Slovak Olympiad 2018, National Round, Problem 5

4/5/2018
Let ABCDABCD an isosceles trapezoid with the longer base ABAB. Denote II the incenter of ΔABC\Delta ABC and JJ the excenter relative to the vertex CC of ΔACD\Delta ACD. Show that the lines IJIJ and ABAB are parallel.
geometrynational olympiad