Question

In an equilateral triangle prove that the centroid and the circum centre coincide

Answer 1

As we know that the centroid divides the median in 2:1 ratio tharefore in equilateral triangle all the medians are equal therefore distance of each vertices from the centroid us equal.
Now as we know that circumcentre is the centre of the circle which passes through all the vertices and the dist of each vertex from the centre is equal (radius) and distance of each vertex is equal from centroid also. Therefore centroid and circumcentre coincides.