MathDB

There are six small circles in the figure with a radius of

1

and tangent to a large circle and the sides of the

ABC

of an equilateral triangle, where touch points are

K, L

and

M

respectively with the midpoints of sides

AB, BC

and

AC

. Find the radius of the large circle and the side of the triangle

ABC

. https://cdn.artofproblemsolving.com/attachments/3/0/f858dcc5840759993ea2722fd9b9b15c18f491.png

Problem Statement