In the figure below, given a triangle
ABC, construct the incircle with incenter I and excircles with
excenters E_{1}, E_{2}, and E_{3}. Let be D, E, F, G, H,
and M the tangent
points of triangle ABC with its excircles. If S_{1}, S'_{1}, S_{2}, S'_{2}, S_{3},
and S'_{3} are
the areas of the shaded triangles, prove that S_{1} = S'_{1},
similarly S_{2} = S'_{2}, and S_{3} = S'_{3}.
View or post a solution.
