MathDB
Geometry: Concurrent lines and concyclic points.

Source: Greece team selection test problem 1

May 3, 2017
geometry

Problem Statement

Let ABCABC be an acute-angled triangle inscribed in circle c(O,R)c(O,R) with AB<AC<BCAB<AC<BC, and c1c_1 be the inscribed circle of ABCABC which intersects AB,AC,BCAB, AC, BC at F,E,DF, E, D respectivelly. Let A′,B′,C′A', B', C' be points which lie on cc such that the quadrilaterals AEFA′,BDFB′,CDEC′AEFA', BDFB', CDEC' are inscribable. (1) Prove that DEA′B′DEA'B' is inscribable. (2) Prove that DA′,EB′,FC′DA', EB', FC' are concurrent.
Back to ProblemsView on AoPS