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A variable plane l x+m y+n z=p(w h e r e...

A variable plane `l x+m y+n z=p(w h e r el ,m ,n` are direction cosines of normal`)` intersects the coordinate axes at points`A ,Ba n dC` , respectively. Show that the foot of the normal on the plane from the origin is the orthocenter of triangle `A B C` and hence find the coordinate of the circumcentre of triangle `A B Cdot`

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