Mathematics - 3D Coordinate Geometry Question with Solution | TestHub

$A(a,0,0),B(0,b,0),C(0,0,c)$ are the mid-points of the sides of $PQR$, so $P(-a,b,c),Q(a,-b,c),R(a,b,-c)$. The median of $△ABC$ is also the median of $△PQR$, so both centroids are $\left(\frac{a}{3},\frac{b}{3},\frac{c}{3}\right).ABC$ is the medial triangle of $PQR$, so the orthocentre of $ABC$ is the circumcentre of $PQR$, and the foot of the perpendicular from $O$ to plane $ABC$ is the orthocentre of $ABC.ar(PQR)=4ar(ABC)=4\cdot \frac{1}{2}\sqrt{a^2{b}^2+b^2{c}^2+c^2{a}^2}$. The incentres do not coincide in general. Options A, B, C are correct.