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Question
D is a point on the side of the BC of ΔABC. Prove that the perimeter of ΔABC is greater than twice of AD.
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Solution
Construction: Join AD
In triangle ACD,
AC + CD > AD ...(i)
(Sum of two of a triangle greater than the third side)
Similarly, in triangle ADB,
AB + BD > AD ...(ii)
Adding (i) and (ii),
AC + CD + AB + BD > AD
AB + BC + AC > 2AD. ...(Since, CD + BD = BC)
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