O is any point in the interior of a triangle ABC then AB + AC is _________.    

Asked by gpnkumar0 | 5th Aug, 2016, 06:24: PM

Expert Answer:

begin mathsize 20px style Construction colon space Produce space BO space to space meet space AC space at space straight D.
Proof colon space
In space increment ABD comma space AB plus AD greater than BD
rightwards double arrow AB plus AD greater than BO plus OD..... left parenthesis straight i right parenthesis
In space increment OCD comma
CD plus DO greater than OC...... left parenthesis ii right parenthesis
left square bracket Sum space of space any space two space sides space must space be space greater space than space the space third space side. right square bracket
Adding space questions space left parenthesis straight i right parenthesis space and space left parenthesis ii right parenthesis comma space we space get
AB plus AD plus CD plus DO greater than BO plus OD plus OC
rightwards double arrow AB plus AC plus DO greater than BO plus OD plus OC
rightwards double arrow AB plus AC greater than BO plus OC end style

Answered by Rebecca Fernandes | 7th Aug, 2016, 10:19: AM