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In △ABC, D is any point on BC. Prove that : AB + BC + AC > 2 AD.

In △ABC, D is any point on BC. Prove that : AB + BC + AC and2 AD. R.S. Aggarwal Mathematics Solutions ICSE Class 9.

Triangles

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Answer

We know that,

In a triangle, sum of any two sides is always greater than the third side.

In △ABD,

⇒ AB + BD > AD …..(1)

In △ACD,

⇒ AC + CD > AD …..(2)

Adding eq.(1) and (2), we have :

⇒ AB + BD + AC + CD > AD + AD

⇒ AB + (BD + CD) + AC > 2AD

⇒ AB + BC + AC > 2AD.

Hence, proved that AB + BC + AC > 2AD.

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