Question

In an acute angled triangle ABC, S is any point on side BC . Prove that AB+ BC + CA › 2AS

Answer 1

TPT:-AB+BC+CA>2AS

PROOF:-

IN TRIANGLE ABS:AB+BS>AS(SUM OF ANY 2 SIDES IS GREATER THEN THE THIRD SIDE).......1

IN TRIANGLE ASC:AC+CS>AS(....AS ABOVE)...2

ADDING 1 AND 2

=AB+BS+AC+CS>AS+AS

=AB+AC+BS+CS>2AS

=AB+AC+AC>2AS (BS+CS=BC)

HENCE PROVED