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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 > 3AD

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D

None of these

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Solution

The correct option is A

AB + BC + CA > 2AD



In Δ ABD, AB + BD > AD (i) (Sum of two sides of a triangle is greater than the third side)
In Δ ACD, AC + DC > AD (ii) (Sum of two sides of a triangle is greater than the third side)
On adding (i) and (ii)
AB + BD + AC + DC > AD + AD
AB + BC + AC > 2AD


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