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Class 9 Maths — Circles

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

Name: ________________________

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

  2. 2.An angle at the circumference standing on an arc is 35°. What is the angle at the centre standing on the same arc, in degrees?

  3. 3.A chord 8 cm long is drawn in a circle of radius 5 cm. Drop a perpendicular from the centre to the chord: the radius to the chord's end is the hypotenuse of the right-angled triangle it makes. How far is the chord from the centre, in centimetres?

  4. 4.The line from the centre of a circle to the mid-point of a chord that is not a diameter is always...

    • a) longer than the radius
    • b) perpendicular to the chord
    • c) the same length as the chord
    • d) parallel to the chord

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

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

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

  7. 7.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

  8. 8.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
    • The region between two radii and the arc joining them
    • The region trapped between a chord and its arc
    • The shorter of the two arcs a chord cuts off
    • A four-sided shape with every corner on the circle

Answer key — Class 9 Maths — Circles

  1. 1. 110
  2. 2. 70
  3. 3. 3
  4. 4. b) perpendicular to the chord
  5. 5. 85
  6. 6. b) Their distances from the centre
  7. 7. 1 — The angle at the centre
  8. 8. 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