If D is any point on the side BC of - ABC- thenA- AB - BC - CA -2 ADB- AB - BC - CA 3 AD

The correct option is A AB + BC + CA gt; 2AD In Δ ABD, AB + BD gt; AD …(i) (Sum of two sides of a triangle is greater than the third side) In Δ ACD, AC ...

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Byju's Answer

Standard X

Mathematics

Relation between Inradius and Perimeter of Triangle

If D is any p...

Question

If D is any point on the side BC of $Δ A B C,$ then

AB + BC + CA > 2AD

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AB + BC + CA < 2AD

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AB + BC + CA > 3AD

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AB + BC + CA = 2AD

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Solution

The correct option is A
AB + BC + CA > 2AD

In $Δ$ ABD, AB + BD > AD $\dots$ (i) (Sum of two sides of a triangle is greater than the third side)
In $Δ$ ACD, AC + DC > AD $\dots$ (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 + (BD + DC) + AC > 2AD
AB + BC + AC > 2AD

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If D is any point on the side BC of ΔABC, then

If D is any point on the side BC of $Δ A B C,$ then