Given positive numbers s_a, s_b, and s_c, the Elkies point is the unique point Y in the interior of a triangle Δ A B C such that the respective inradii r_a, r_b, r_c of the triangles Δ B Y C, Δ C Y A, and Δ A Y B satisfy r_a :r_b :r_c = s_a :s_b :s_c.

congruent incircles point | inradius