Geometric Ineq

For discussing Olympiad level Geometry Problems
Atonu Roy Chowdhury
Posts: 40
Joined: Fri Aug 05, 2016 7:57 pm

Geometric Ineq

Let $h_a$, $h_b$, $h_c$ be the lengths of the altitudes from $A$, $B$, $C$ respectively of a triangle $ABC$. Let $P$ be any point inside the triangle. Prove that
$\frac{PA}{h_b+h_c} + \frac{PB}{h_c+h_a} + \frac{PC}{h_a+h_b} \ge 1$

Atonu Roy Chowdhury
Posts: 40
Joined: Fri Aug 05, 2016 7:57 pm