Question

a 10 rupee coin is placed on a flat surface . if more 10 rupee coins are to be placed encircling around it such that each coin touches the adjacent one ,then how many more coins are required ?​

Answer 1

Answer:

Let the radius of the coin be x.

Since each coin touches the middle one, then the distance between centres has to be 2x

Since each coin touches it's adjacent( not the middle one), hence the distance between them is also 2x.

Here considering each coin as the vertex of a polygon, considering above facts, we must be looking at a regular polygon with each side being 2x.

Since distance from centroid(center of the middle coin) to any other vertex(center of other coins) is also 2x, only polygon which satisfies this condition has to be hexagon.