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Question
AD is a median of the triangle ABC. Is it true that AB + BC + CA > 2AD? Give reason for your answer.
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Solution
In triangle ABD,
AB + BD > AD ...(i)
AC + CD > AD ...(ii) [Sum of the length of any two sides of a triangle must be greater must be greater that the third side]
Adding (i) and (ii), we get
AB + BD + CD + AC > 2AD
AB + BC + CA > 2AD ...[BD = CD as AD is median of triangle ABC]
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