AD,BE तथा CF, `DeltaABC` की माधिकाये हे| तब सही कथन ज्ञात करे?

Options

A. `(AD+BE+CF) lt AB+BC+CA`
B. `(AD+BE+CFgtAB+BC+CA)`
C. `AD+BE+CF=AB+BC+CA`
D. `AD+BE+CF=sqrt(2)(AB+BC+CA)`

Answer

C

Explanation

According to question,

Points D,E,F are midpoints of BC, CA and AB.
`therefore AB+ACgt2AD`………..(i)
AB+BC `gt2BE`…………..(ii)
`BC+CAgt2CF`……………(iii)
Adding to equation (i),(ii) and (iii) we get
`2(AB+BC+CA) gt 2(AD+BE+CF)`
`therefore (AB+BC+CA)gt(AD+BE+CF)`