Question

If D is any point on the side BC of $\Delta ABC$, then

• A. AB + BC + CA > 2AD
• B. AB + BC + CA < 2AD
• C. AB + BC - CA > 2AD
• D. AB + BC + CA = 2AD

Answer 1

The correct option is A AB + BC + CA > 2AD


Sum of two sides of a triangle is greater than the third side.

In $\Delta ABD$, AB + BD > AD $\cdots$ (i)
In $\Delta ACD$, AC + DC > AD $\cdots$ (ii)

On adding (i) and (ii),
AB + BD + DC +AC > AD + AD
But BD + DC = BC.
$\Rightarrow$ AB + BC + AC > 2AD