Circle vocabulary Worked Solutions — GCSE Maths

Fully worked, step-by-step solutions to GCSE Circle vocabulary questions. See exactly how to solve problems on circle vocabulary, classifying a line segment, naming parts of a circle, circumference.

circle vocabularyclassifying a line segmentnaming parts of a circlecircumferencesectors and segmentscentre
GCSE Foundation70 questionsStep-by-step solutions
Question 1
1 markeasy
The diagram shows a circle with centre O(0,0)O(0,0) and radius 55 cm. The point A(3,4)A(3,4) lies on the circle. What is the correct mathematical name for the line segment OAOA?

Worked solution

  1. Write down what the diagram gives you

    O(0, 0),r=5 cmO(0,\,0), \qquad r = 5\text{ cm}

    Every circle word is decided by where the ends of the line lie, so start from the centre O(0,0)O(0,0) and the radius r=5r = 5 cm.

  2. Look at where each end of the segment lies

    O is the centre,OA2=32+42=25=52O \text{ is the centre}, \qquad OA^2 = 3^2 + 4^2 = 25 = 5^2

    One end is the centre. The other end AA satisfies OA2=25=52OA^2 = 25 = 5^2, so OA=5OA = 5 cm and AA lies on the circle.

  3. Name the segment

    radius\text{radius}

    OAOA joins the centre OO to the point AA on the circle, so it is a radius.

Answer
radius\text{radius}
Question 2
1 markeasy
The diagram shows a circle with centre O(0,0)O(0,0) and radius 1010 cm. The points A(6,8)A(6,8) and B(−6,−8)B(-6,-8) lie on the circle. What is the correct mathematical name for the line segment ABAB?

Worked solution

  1. Write down what the diagram gives you

    O(0, 0),r=10 cmO(0,\,0), \qquad r = 10\text{ cm}

    Every circle word is decided by where the ends of the line lie, so start from the centre O(0,0)O(0,0) and the radius r=10r = 10 cm.

  2. Check that both ends lie on the circle

    OA2=62+82=100=102,OB2=−62+−82=100=102OA^2 = 6^2 + 8^2 = 100 = 10^2, \qquad OB^2 = -6^2 + -8^2 = 100 = 10^2

    Both OA=10OA = 10 cm and OB=10OB = 10 cm, so AA and BB are both points of the circle.

  3. Name the segment

    diameter\text{diameter}

    Both ends lie on the circle and the segment passes through the centre, so ABAB is a diameter, of length 2020 cm.

Answer
diameter\text{diameter}
Question 3
1 markeasy
The diagram shows a circle with centre O(0,0)O(0,0) and radius 55 cm. The points A(3,4)A(3,4) and B(5,0)B(5,0) lie on the circle. What is the correct mathematical name for the line segment ABAB?

Worked solution

  1. Write down what the diagram gives you

    O(0, 0),r=5 cmO(0,\,0), \qquad r = 5\text{ cm}

    Every circle word is decided by where the ends of the line lie, so start from the centre O(0,0)O(0,0) and the radius r=5r = 5 cm.

  2. Check that both ends lie on the circle

    OA2=32+42=25=52,OB2=52+02=25=52OA^2 = 3^2 + 4^2 = 25 = 5^2, \qquad OB^2 = 5^2 + 0^2 = 25 = 5^2

    Both distances from the centre are 55 cm, so AA and BB are both points of the circle.

  3. Name the segment

    chord\text{chord}

    Both ends lie on the circle and the segment does not pass through the centre, so ABAB is a chord.

Answer
chord\text{chord}
Question 4
2 markseasy
The diagram shows a circle with centre O(0,0)O(0,0) and radius 55 cm. The points A(−1,7)A(-1,7) and B(7,1)B(7,1) both lie outside the circle. What is the correct mathematical name for the line segment ABAB?

Worked solution

  1. Write down what the diagram gives you

    O(0, 0),r=5 cmO(0,\,0), \qquad r = 5\text{ cm}

    Every circle word is decided by where the ends of the line lie, so start from the centre O(0,0)O(0,0) and the radius r=5r = 5 cm.

  2. Check where the two ends lie

    OA2=50>25=r2,OB2=50>25=r2OA^2 = 50 > 25 = r^2, \qquad OB^2 = 50 > 25 = r^2

    Both ends are further than 55 cm from the centre, so AA and BB lie outside the circle. Neither end is on the circle, so the segment is not a chord, a diameter or a radius.

  3. Name the segment

    tangent\text{tangent}

    The line meets the circle at exactly one point T(3,4)T(3,4) and is perpendicular to the radius OTOT there, so ABAB is a tangent.

Answer
tangent\text{tangent}
Question 5
1 markeasy
The diagram shows a circle with centre O(0,0)O(0,0) and radius 55 cm. The points A(3,4)A(3,4) and B(5,0)B(5,0) lie on the circle. What is the correct mathematical name for the shorter curved part of the circle joining AA and BB?

Worked solution

  1. Write down what the diagram gives you

    O(0, 0),r=5 cmO(0,\,0), \qquad r = 5\text{ cm}

    The part named is drawn on the edge of the circle, so decide first whether it is a line, a curve or a region.

  2. Check that both ends lie on the circle

    OA2=25=52,OB2=25=52OA^2 = 25 = 5^2, \qquad OB^2 = 25 = 5^2

    AA and BB are both points of the circle, and the part named runs along the curved edge between them.

  3. Name the part of the circle

    arc\text{arc}

    It is a piece of the curved edge between two points of the circle, so it is an arc (here, the minor arc ABAB).

Answer
arc\text{arc}

Unlock 65 more Circle vocabulary questions

Create a free account to work through every GCSE Circle vocabulary question with instant step-by-step worked solutions, progress tracking and interactive lessons.

  • Full worked solutions for every question
  • Interactive lessons and instant feedback
  • Track your mastery across every topic
Create a Free Account

No card required · Free forever

More Circle vocabulary practice

Hard QuestionsPractice Questions

Related Geometry & Measures topics

3D solids, plans and elevations3D Pythagoras and trigonometryAngle factsArcs and sectorsBearings and scale drawingsCircle theorems