Question

If the orthocentre, centroid and the circumcentre of a triangle $ABC$ coincide with each other and if the length of side $AB$ is $8\sqrt{3}$, then the length of the altitude through the vertex $A$ is

Answer 1

Here, if the orthocentre, centroid and the circumcentre of a triangle $ABC$ coincide with each other, then the triangle will be equilateral triangle
Length of side $=8\sqrt{3}\text{units}$
Altitude $=\frac{\sqrt{3}}{2}a$
$=\frac{\sqrt{3}}{2}\times 8\sqrt{3}=12\text{units}$