Question

- O is a point in the exterior of A ABC. What symbol >, '<' or '=' will you use to
complete the statement OA + OB
AB ?
Write two other similar statements and show that
1
OA + OB + OC > (AB + BC + CA)
2​

Answer 1

Answer:

We know that the sum of any two sides of a triangle is always greater than the third side, in △OAB, we have, OA + OB > AB ….. (i) OB + OC > BC …… (ii) OA + OC > CA ….. (iii) On adding equations (i), (ii) and (iii) we get: OA + OB + OB + OC + OA + OC > AB + BC + CA 2(OA + OB + OC) > AB + BC + CA OA + OB + OC > (AB + BC + CA)/2 Or OA + OB + OC > ½ (AB + BC +CA) Hence the proof.Read more on Sarthaks.com - https://www.sarthaks.com/688319/is-point-in-the-exterior-of-abc-what-symbol-or-will-you-see-to-complete-the-statement-oa-ob-ab