O is any point in the interior of ΔABC. Prove that (i) AB+AC>OB+OC (i

1.	O is any point in the interior of ΔABC. Prove that (i) AB+AC>OB+OC (ii) AB+BC+CA>OA+OB+OC (iii) OA+OB+OC>12(AB+BC+CA)
Answer» O is any point in the interior of $Δ A B C .$ Prove that $(i) A B + A C > O B + O C$ $(i i) A B + B C + C A > O A + O B + O C$ $(i i i) O A + O B + O C > \frac{1}{2} (A B + B C + C A)$

O is any point in the interior of ΔABC. Prove that (i) AB+AC>OB+OC (ii) AB+BC+CA>OA+OB+OC (iii) OA+OB+OC>12(AB+BC+CA)

Answer»

O is any point in the interior of $Δ A B C .$

Prove that

$(i) A B + A C > O B + O C$

$(i i) A B + B C + C A > O A + O B + O C$

$(i i i) O A + O B + O C > \frac{1}{2} (A B + B C + C A)$