If D is any point on the side BC of triangle ABC. Show that AB+BC+CA>2AD.
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Answer:
In ABD , By Inequality property of triangle
AB + BD > AD ----------(1)
And In ACD ,By Inequality property of triangle
DC + AC > AD ---------(2)
On Adding Eq (1) and Eq (2)
AB+BD+DC+AC> AD+AD
AB + BC + AC > 2 AD [Given BD+DC = BC]
AB + BC + AC > 2 AD
hence Proved
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