The figure below shows a triangle ABC with the excenters E1, E2, and E3.
Lines AE1, BE2, and CE3 meet
circumcircle O at A1, B1, and C1,
respectively. If S1, S2, and
S3 are the areas of triangle E1E2E3,
and triangle A1B1C1,
respectively, prove that
S1 = 2.S2 = 4.S3.
Kaleidoscope of Problem 1112 base on Poincare Disk Model.