The center of the circumference belongs to subtopics that make up the topic of the circumference and the circle. We use the concept of the center of the circumference to define the circumference itself, as well as to calculate the radius and diameter of each given circumference.

The center of the circumference, as its name indicates, is a point located in the center of the circumference. It is usually customary to mark this point with the letter O. Indeed, this point is at the same distance from each of the points that make up the circumference.

The formula for the area of a rhombus (the square is also a rhombus). In the square, the diagonals are equal and therefore all the diagonals are $9\operatorname{cm}$

$A_2=\frac{9\cdot9}{2}=\frac{81}{2}=40.5$

$A=20.25\pi-40.5=$

$=20.25\cdot3.14-40.5=$

$23.085\operatorname{cm}²$

Answer

$23.085\operatorname{cm}²$

Exercise 5

Assignment

The trapezoid $ABCD$ is inside the circle, whose center $O$

The area of the circle is $16\pi\operatorname{cm}²$

What is the area of the trapezoid?

Solution

$A_o=\pi r^2=16\pi$

We cancel out the 2 pi and take the square root

$r=\sqrt{16}=4$

$DC=DO+OC=$

$R+R=2R=$

$2\cdot4=8$

$ABCD=\frac{(AB+CD)EO}{2}=$

$\frac{(5+8)3.5}{2}=$

$\frac{13\cdot3.5}{2}=22.75$

Answer

$22.75\operatorname{cm}²$

Check your understanding

Question 1

All ____ about the circle located in the distance ____ from the ____ circle

The center of a circle is the midpoint that is at the same distance from the circumference to that point, it is exactly in the middle of the circumference.

What is the diameter of a circle?

It is the line that touches the circumference from end to end but passes through the center, as shown in the following image.

Do you think you will be able to solve it?

Question 1

Given that the radius of a circle is 0.5 cm, the length of the diameter is 10 cm

The circumference has some lines, which are presented in the image and let's define each one of them:

C (Center): It is the point that is at the center of the circumference

D (Diameter): It is the line that passes through the midpoint of the circumference, that is, it passes through the center and touches the circumference from end to end.

R (Radius): It is half of the diameter, and this line only touches the center at one point of the circumference.

CU (Chord): It is the line that touches the circumference from end to end but does not necessarily pass through the center.

S (Secant): Line that crosses the circumference, as shown in the image:

What happens if the radius is equal to zero?

If the radius in this case is zero, then there is no circumference, since as we mentioned the radius is the line that goes from the center of the circumference to any point on it, and because in this case the radius equals zero, we are not drawing any line and therefore no circle.

Test your knowledge

Question 1

Is it possible for the circumference of a circle to be \( 10\pi \) if its diameter is \( 2\pi \) meters?