Lines a1,b1,c1 pass through the vertices A,B,C respectively of a triange ABC; a2,b2,c2 are the reflections of a1,b1,c1 about the corresponding bisectors of ABC; A1=b1∩c1,B1=a1∩c1,C1=a1∩b1, and A2,B2,C2 are defined similarly. Prove that the triangles A1B1C1 and A2B2C2 have the same ratios of the area and circumradius (i.e. R1S1=R2S2, where Si=S(△AiBiCi), Ri=R(△AiBiCi)) geometryisogonalscircumcircle