$\mathrm{A}\mathrm{B}\mathrm{C}$ is a triangle. Locate a point in the interior of $∆\mathrm{ABC}$ which is equidistant from all the vertices of $∆\mathrm{ABC}$.

In a huge park, people are concentrated at three points as shown in the figure.
A: Where there are different slides and swings for children.
B: near which a man made lake is situated.
C: Which is near to a large parking and exit.
Where should an ice-cream parlor be set up so that maximum number of persons can approach it?

Complete the hexagonal shaped rangolis by filling them with as many equilateral triangles of side 1 $\mathrm{cm}$ as you can. Count the number of triangles in each case. Which has more triangles?