Mathematics - 3D-Coordinate Geometry Question with Solution | TestHub

OP is normal to the plane, so the plane is $ax+by+cz=p^2$, with $A\left(\frac{p^2}{a},0,0\right),B\left(0,\frac{p^2}{b},0\right)$, $C\left(0,0,\frac{p^2}{c}\right)$. The area of $△ABC$ is $\sqrt{A_{xy}^2+A_{yz}^2+A_{zx}^2}$ where $A_{xy}=\frac{p^4}{2|ab|},A_{yz}=\frac{p^4}{2|bc|}$, $A_{zx}=\frac{p^4}{2|ca|}$. So the area is $\frac{p^4}{2}\sqrt{\frac{a^2+b^2+c^2}{a^2{b}^2{c}^2}}=\frac{p^5}{2|abc|}$.