# The Parts of a Circle - Examples, Exercises and Solutions

The perpendicular to the chord comes out of the center of the circle, intersecting the chord, the central angle in front of the chord and the arc in front of the chord.
Moreover, if there is a section that comes out from the center of the circle and crosses the chord, it will also be perpendicular to the chord.

We are here to present the properties of the perpendicular from the center of the circle to the chord.
First, we will remember that the perpendicular is a line that forms a $90°$ degree angle.
Let's see it in the illustration:

In front of us, there is a circle.
We will mark the center of the circle with a letter $A$
Our chord will be blue and will be called $BC$.
The vertical, which comes out from the center of the circle and will be perpendicular to the chord $BC$.
We will mark it in red and call it $AD$.

## Practice The Parts of a Circle

### Exercise #1

In which of the circles is the point marked in the circle and not on the circumference?

### Exercise #2

In which of the circles is the segment drawn the radius?

### Exercise #3

How many times longer is the radius of the red circle than the radius of the blue circle?

5

### Exercise #4

How many times longer is the radius of the red circle, which has a diameter of 24, than the radius of the blue circle, which has a diameter of 12?

2

### Exercise #5

How many times longer is the radius of the red circle than the radius of the blue circle?

### Video Solution

$2$

### Exercise #1

Calculate the length of the arc marked in red given that the circumference is 6.

### Video Solution

$\frac{5}{6}$

### Exercise #2

Calculate the length of the arc marked in red given that the circumference is 36.

2

### Exercise #3

Calculate the length of the arc marked in red given that the circumference is 12.

2

### Exercise #4

Calculate the length of the arc marked in red given that the circumference is 12.

8

### Exercise #5

Calculate the length of the arc marked in red given that the circumference is equal to 24.

### Video Solution

$10$

### Exercise #1

Calculate the area of the section painted red given that the area of the circle is 12.

8

### Exercise #2

How many times longer is the radius of the red circle than the radius of the blue circle?

### Video Solution

$2\frac{1}{2}$

### Exercise #3

How many times longer is the radius of the red circle (14 cm) than the radius of the blue circle, which has a diameter of 7?

4

### Exercise #4

Calculate the length of the arc marked in red given that the circumference is 18.

13

### Exercise #5

Calculate the length of the arc marked in red given that the circumference is 6.

### Video Solution

$\frac{5}{6}$