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Year 9 Maths — Circles

Use the chord, arc and cyclic-quadrilateral facts to find angles and lengths in a circle.

Name: ________________________

  1. 1.Match each word to what it names in a circle.

    • Major arc
    • Minor arc
    • Segment
    • Sector
    • Cyclic quadrilateral
    • The longer of the two arcs a chord cuts off
    • A four-sided shape with every corner on the circle
    • The shorter of the two arcs a chord cuts off
    • The region trapped between a chord and its arc
    • The region between two radii and the arc joining them

  2. 2.The chord AB has an angle drawn on it at the centre of the circle, and another at the point C up on the circle. Tap the angle at the centre.

    Write the number of the part.

    12

  3. 3.In cyclic quadrilateral ABCD, angle A is 70° and angle B is 100°. How big is angle C, in degrees?

  4. 4.The longest chord that can be drawn in a circle has a name of its own. What is it? One word.

  5. 5.Two chords of a circle are equal in length. What else must be equal?

    • a) Their distances from the centre
    • b) Their distances from each other
    • c) The two arcs on either side of each chord
    • d) Their angles at every point of the circle

  6. 6.An angle drawn in a semicircle is always how many degrees?

  7. 7.One angle of a cyclic quadrilateral is 95°. How big is the angle opposite it, in degrees?

  8. 8.Sort each statement about a circle by whether it is always true.

    Groups: Always true · Not always true

    • All the chords of a circle are the same length
    • The perpendicular from the centre to a chord cuts the chord in half
    • The angle in a semicircle is a right angle
    • The angle at the centre equals the angle at the circumference on the same arc
    • Opposite angles of a cyclic quadrilateral add up to 180°
    • Every chord passes through the centre

Answer key — Year 9 Maths — Circles

  1. 1. Major arc → The longer of the two arcs a chord cuts off; Minor arc → The shorter of the two arcs a chord cuts off; Segment → The region trapped between a chord and its arc; Sector → The region between two radii and the arc joining them; Cyclic quadrilateral → A four-sided shape with every corner on the circle
  2. 2. 1 — The angle at the centre
  3. 3. 110
  4. 4. diameter
  5. 5. a) Their distances from the centre
  6. 6. 90
  7. 7. 85
  8. 8. The perpendicular from the centre to a chord cuts the chord in half → Always true; The angle in a semicircle is a right angle → Always true; Opposite angles of a cyclic quadrilateral add up to 180° → Always true; Every chord passes through the centre → Not always true; The angle at the centre equals the angle at the circumference on the same arc → Not always true; All the chords of a circle are the same length → Not always true