In a \(\Delta\)ABC if \(P\) is any interior point inside it, Find the minimum value of :

\(\displaystyle \text{min}(BC.PA^2+CA.PB^2+AB.PC^2)\)

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## Comments

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TopNewestkeep 3 masses of values BC,CA,AB at points A,B,C. Moment of inertia about any point P is given by (BC.PA^2+...)which is what we have to minimize. However moment of inertia is minimum at centre of mass so we find centre of mass whose coordinates are Same as formula of coordinates of incentre given sides. So the required point P is its incentre

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Yep, That's a great observation.

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What was ur solution?

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Awesome solution!

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