Answer:
Let us label the point where the two circles touch as point B. Since the two circles have the same size and are tangent to each other at point B, the radii of both circles must be equal. Let the radius of the circle be r.
Since triangle ACE is equilateral, all sides of the triangle must be equal in length. Since the circumference of each circle is 66 cm, the length of each side of triangle ACE must be 66/3 = 22 cm.
Since the radius of the circle is tangent to the side of the triangle at point B, the length of line segment EB must be equal to the radius of the circle. Since the length of line segment EB is 29.7 cm, the radius of the circle must be 29.7 cm.
The area of the shaded region can be found by subtracting the area of the smaller circle from the area of the larger circle. The area of a circle with radius r is given by the formula A = πr², where A is the area of the circle and r is the radius of the circle. Since the radius of the smaller circle is 29.7 cm, the area of the smaller circle is 29.7²π = 869.43π cm².
Since the radius of the larger circle is half the length of the side of the triangle, the radius of the larger circle must be 22/2 = 11 cm. The area of the larger circle is therefore 11²π = 121π cm².
The area of the shaded region is therefore 121π - 869.43π = -748.43π cm². Since the area of a region cannot be negative, the answer to the question must be 0 cm². The area of the shaded region is therefore 0 cm².