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?

Video Solution

Answer

Exercise #2

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

Video Solution

Answer

Exercise #3

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

240

Video Solution

Answer

8

Exercise #4

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

60°60°60°

Video Solution

Answer

2

Exercise #5

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

50

Video Solution

Answer

56 \frac{5}{6}

Exercise #1

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

240

Video Solution

Answer

8

Exercise #2

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

20

Video Solution

Answer

2

Exercise #3

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

220

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Answer

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?

Video Solution

Answer

2

Exercise #5

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

168

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Answer

2 2

Exercise #1

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

150°150°150°

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Answer

10 10

Exercise #2

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

260°260°260°

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Answer

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?

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Answer

4

Exercise #4

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

210

Video Solution

Answer

212 2\frac{1}{2}

Exercise #5

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

20°20°20°

Video Solution

Answer

2 2

Topics learned in later sections

  1. Circle
  2. Distance from a chord to the center of a circle
  3. Chords of a Circle
  4. Central Angle in a Circle
  5. Arcs in a Circle
  6. Perpendicular to a chord from the center of a circle
  7. Inscribed angle in a circle
  8. Area of a circle
  9. The Circumference of a Circle
  10. How is the radius calculated using its circumference?