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Question

If D is any point on the side BC of ΔABC, then

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

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

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

In ΔABD, AB + BD > AD (i)
In ΔACD, AC + DC > AD (ii)

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

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