Find all $P$ points inside $ABCD$ tetrahedron, so that $V_{ABCP} = V_{ABDP}$
Thanks in advance for any help.
Find all $P$ points inside $ABCD$ tetrahedron, so that $V_{ABCP} = V_{ABDP}$
Thanks in advance for any help.
Express the volumes: $ V[ABCP]=\frac{1}{3} d(P,ABC) Area(ABC),\ V[ABDP]=\frac{1}{3} d(P,ABD) Area(ABD)$
The equality of the two volumes prove that $ \frac{d(P,ABC)}{d(P,ABD)}=\frac{Area(ABC)}{Area(ABD)}$
So the distances from $P$ to the planes $ABC$ and $ABD$ are proportional. I think the locus is a plane, but try and see it for yourself.