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Question

If D is any point on the side BC of ΔABC, then which of the inequality holds true?

A
AB+BC+CA>2AD
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B
AB+BC+CA<2AD
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C
AB+BCCA>2AD
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D
AB+BC+AC=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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