Three circular rings of equal radii of $1 \mathrm{cm}$ each are touching each other. A string runs all around the set of rings very tightly. What is the minimum length of string required to bind all the three rings in the given manner?

 

An equilateral triangle circumscribes all the three circles each of radius $1\mathrm{cm}$. What is the perimeter of the equilateral triangle?

Six circles each of unit radius are being circumscribed by another larger circle. All the smaller circles touch each other. What is the circumference of the larger circle?

There are six circular rings of iron, kept close to each other. A string binds them as tightly as possible. If the radius of each circular iron ring is $1 \mathrm{cm}$. What is the minimum possible length of string required to bind them?

An equilateral triangle circumscribes all the six circles, each with radius $1 \mathrm{cm}$. What is the perimeter of the equilateral perimeter of the equilateral triangle?

In a right angle triangle $\mathrm{ABC}$, what is the maximum possible area of a square that can be inscribed when one of its vertices coincide with the vertex of the right angle of the triangle?

In the adjoining figure, a square of maximum possible area is circumscribed by the right-angle triangle $\mathrm{ABC}$ in such a way that one of its sides just lies on the hypotenuse of the triangle. What is the area of the square?