Practice30Create account

From a point O inside triangle ABC, segments OA, OB, OC are drawn.
It can be proved that OA + OB + OC is greater than which quantity?

Class 9Inequalities in a TriangleGeometry — Triangles
  • Ahalf the perimeter of triangle ABC
  • Bthe full perimeter of triangle ABC
  • Ctwice the perimeter
  • Dthe longest side only

Step-by-Step Solution

Using triangle inequality in triangles OAB, OBC, OCA: OA+OB>AB, OB+OC>BC, OC+OA>CA. Adding: 2(OA+OB+OC) > AB+BC+CA, so OA+OB+OC > .
Answer: A) half the perimeter of triangle ABC

Master this chapter in 30 minutes a day.

Don't just memorise the answer — build a daily practice habit.

Practice 5 Similar Questions Free →

All Inequalities in a Triangle practice questions

More Class 9 Inequalities in a Triangle practice

AD is drawn from A perpendicular to BC in triangle ABC, with D on BC. Which of these is…The sides of triangle ABC are AB = 5 cm, BC = 6 cm and CA = 7 cm. Arrange the three…A triangle has two sides measuring 10 cm and 10 cm. For how many integer values of the…For triangle ABC, it is given that angle A < angle B < angle C. Kavya says CA < AB < BC.…Sides of a triangle are (x), (x + 2) and (x + 4) cm, where x is a positive integer. What…