if o is any point in the interior od triangleABC PROVE OA +OB+OC 1/2(AB+BC+CA) - Maths - Lines and Angles

Question

if o is any point in the interior od triangleABC PROVE OA
+OB+OC>1/2(AB+BC+CA)

Soumil Rana · Accepted Answer

It is such a easy question --===

AB < AO + BO ( Sum of 2 sides of triangle is greater than
3)
AC < AO + CO ( Sum of 2 sides of triangle is greater than
3)
BC < BO + CO ( Sum of 2 sides of triangle is greater than
3)

NOW ON ADDING LHS AND RHS WE GET -

AB + AC + BC < AO + BO + AO + CO + BO + CO
AB + AC + BC < 2AO + 2BO + 2CO
AB + AC + BC < 2(AO + BO + CO)
FINAL ANS = 1/2(AB + AC + BC) < AO + BO + CO

if o is any point in the interior od triangleABC.PROVE OA +OB+OC>1/2(AB+BC+CA)