Question 13
Prove that, in every scalene triangle,
$$
\frac{h_a - h_b}{r_b - r_a} + \frac{h_b - h_c}{r_c - r_b} + \frac{h_c - h_a}{r_a - r_c} \ge \frac{3}{2}.
$$
$$
\frac{h_a - h_b}{r_b - r_a} + \frac{h_b - h_c}{r_c - r_b} + \frac{h_c - h_a}{r_a - r_c} \ge \frac{3}{2}.
$$