Answer
$E = \frac{Q}{3\pi \epsilon_0~d^2}$
Work Step by Step
Suppose the points $A, B,$ and $C$ form an equilateral triangle.
We can consider the electric field at the midpoint of $B$ and $C$
The electric fields due to $B$ and $C$ have the same magnitude and point in opposite directions. Therefore, they cancel with each other.
The net electric field at the midpoint will be the electric field due to point $A$
We can find the distance $r$ between $A$ and the midpoint:
$r = \sqrt{d^2-(\frac{d}{2})^2}$
$r = \frac{\sqrt{3}}{2}~d$
We can find the magnitude of the electric field:
$E = \frac{Q}{4\pi\epsilon_0~r^2}$
$E = \frac{Q}{4\pi \epsilon_0~(\frac{\sqrt{3}}{2}~d)^2}$
$E = \frac{Q}{3\pi \epsilon_0~d^2}$
