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Let ABC be a triangle whose centroid is ...

Let ABC be a triangle whose centroid is G, orthocentre is H and circumcentre is the origin 'O'. If D is any point in the plane of the triangle such that no three of O,A,C and D are collinear satisfying the relation. AD+BD+CH+3HG=`lamdaHD`, then what is the value of the scalar `lamda`.

Text Solution

Verified by Experts

The correct Answer is:
2
`LHS=d-a+d-b+h-c+3(g-h)`
`=2d-(a+b+c)+3((a+b+c))/(3)-2h`
`=2d-2h=2(d-h)=2HDimplies lamda=2.`
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