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

A tangent to a circle is a line that touches the circle at one point.

Tangent Theorem:

1) The tangent to the circle is perpendicular to the radius at the starting point

2) Every line perpendicular to the radius at its end is tangent to the circle

3) The angle between the tangent and any chord is equal to the circumferential angle that rests on that chord on the other side.

4) Two tangents to the circle that come out from the same point are equal to each other.

5) A segment that passes between the center of the circle and the point from which two tangents to the circle come out, cuts the angle between the tangents.

6) If from any point outside the circle, a tangent comes out and cuts the circle, then the product of the entire tangent on its outside is equal to the square of the tangent.

7) In the triangle that encloses the circle, the three bisectors of the angles of the triangle meet at a point in the center of the circle.

8) We can determine that a convex quadrilateral encloses a circle only if - the sum of two opposite sides in the square will be equal to the sum of the other two sides in the square.

## Practice The Parts of a Circle

### Exercise #1

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

### Exercise #2

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

### Exercise #3

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

8

### Exercise #4

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

2

### Exercise #5

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

### Video Solution

$\frac{5}{6}$

### Exercise #1

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

8

### Exercise #2

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

2

### 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 equal to 24.

### Video Solution

$10$

### Exercise #2

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

13

### 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

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 #5

Calculate the area of the section shaded in red given that the area of the circle is 36.

### Video Solution

$2$