To prove anything about a shape or object, we need to define what we mean by "C2 with a square of length 10x+1".
Assuming that C2 is a circle with a circumference of 2, and x is equal to 0, then the square with a length of 10x+1 would have a length of 1.
In this case, the statement to prove would be: "The circle C2 with a square of length 1 (circumscribed around the circle) has an area greater than or equal to the area of the circle."
To prove this statement, we can use the formula for the area of a circle (A = πr^2), where r is the radius of the circle. We know that the circumference of C2 is 2, so we can find the radius using the formula for the circumference of a circle (C = 2πr):
2 = 2πr
r = 1/π
Substituting this value of r into the formula for the area of a circle, we get:
A = π(1/π)^2
A = 1/π
Therefore, the area of C2 is 1/π.
Next, we need to find the area of the square with a length of 1. The formula for the area of a square is A = s^2, where s is the length of a side. In this case, the length of a side is 1, so the area of the square is:
A = 1^2
A = 1
Comparing the area of the circle and the area of the square, we have:
1/π ≥ 1
Since π is approximately 3.14, we can see that 1/π is greater than 1. Therefore, the circle C2 with a square of length 1 (circumscribed around the circle) has an area greater than the area of the square.
Therefore, we have proven that C2 with a square of length 10x+1 (where x is 0) has a circle with an area greater than the area of the square.