MathDB

3

Part of 2010 Greece National Olympiad

Problems(1)

Concyclic points

Source: Greek olympiad - 2010, senior , today, problem - 3

2/27/2010
A triangle ABC ABC is inscribed in a circle C(O,R) C(O,R) and has incenter I I. Lines AI,BI,CI AI,BI,CI meet the circumcircle (O) (O) of triangle ABC ABC at points D,E,F D,E,F respectively. The circles with diameter ID,IE,IF ID,IE,IF meet the sides BC,CA,AB BC,CA, AB at pairs of points (A1,A2),(B1,B2),(C1,C2) (A_1,A_2), (B_1, B_2), (C_1, C_2) respectively.
Prove that the six points A1,A2,B1,B2,C1,C2 A_1,A_2, B_1, B_2, C_1, C_2 are concyclic.
Babis
geometryincentercircumcirclepower of a pointradical axisgeometry proposed