Question

let o be any interior point of an equilateral triangle ABC .Show that 2(OA+OB+OC)>3AB​

Answer 1

Answer:

2(OA + OB + OC) > 3AB

Step-by-step explanation:

Let o be any interior point of an equilateral triangle ABC .Show that 2(OA+OB+OC)>3AB​

O is interior point of an equilateral triangle ABC

Three triangles are formed by O

ΔOAB  , ΔOBC  & ΔOCA

in any trinagle sum of two sides > third side

=>

in ΔOAB  OA + OB  > AB

in ΔOBC  OB + OC > BC

& in ΔOCA  OC  + OA > AC

Adding all three

OA + OB + OB + OC + OC + OA  > AB + BC + AC

ΔABC is equilateral => AB = BC = AC

=> 2OA + 2OB + 2OC > AB + AB + AB

=> 2(OA + OB + OC) > 3AB

QED

Proved