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

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

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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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 – Ajinkya Shivashankar · 3 weeks ago

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– Aditya Sharma · 2 weeks, 6 days ago

Yep, That's a great observation.Log in to reply

– Harsh Shrivastava · 2 weeks, 6 days ago

What was ur solution?Log in to reply

– Aditya Sharma · 2 weeks, 6 days ago

That used the Erdos-Mordell inequality and then some co-ordinate, anyways his observation from physics outweighs mine here.Log in to reply

– Harsh Shrivastava · 3 weeks ago

Awesome solution!Log in to reply