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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