Let a, b, c be three edges of a triangle, D be the triangle's 面積.

Let r be 內心半徑，a = y + z，b = z + x， c = x + y，and s = x+y+z。

Then, abc = (y + z)(z + x)(x + y) >= 8xyz = 8(s-a)(s-b)(s-c). (算術平均＞＝幾何平均）

We have sabc >= 8s(s-a)(s-b)(s-c), which implies R = abc/(4D) = 2D/s = r.

請問：如何證明 R = (abc)/4D？