Elkies Point

Given Positive numbers $s_a$, $s_b$, and $s_c$, the Elkies point is the unique point $Y$ in the interior of a Triangle $\Delta ABC$ such that the respective Inradii $r_a$, $r_b$, $r_c$ of the Triangles $\Delta BYC$, $\Delta CYA$, and $\Delta AYB$ satisfy $r_a:r_b:r_c = s_a:s_b:s_c$.

See also Congruent Incircles Point, Inradius

References

Kimberling, C. ``Central Points and Central Lines in the Plane of a Triangle.'' Math. Mag. 67, 163-187, 1994.

Kimberling, C. and Elkies, N. ``Problem 1238 and Solution.'' Math. Mag. 60, 116-117, 1987.