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CBSE Worksheet for chapter- 10 Circle class 10

Worksheet For class 10

Find CBSE Worksheet for chapter- 10 Circle class 10

SUMMARY

  • Theorem 1: The perpendicular from the centre of a circle to a chord bisects the chord.
  • Theorem 2: There is one and only one circle passing through three given non-collinear points.
  • Theorem 3: the angle subtended by an arc at the centre is double the angle subtended by it at any point on the remaining part of the circle.
  • Theorem 4: Angles in same segment of a circle are equal.
  • Theorem 5: angle in the semicircle is a right angle.
  • Theorem 6: the sum of either pair of opposite angles of a cyclic quadrilateral is 180°.
  • Theorem 7: Equal chords of a circle (or of congruent circles) are equidistant from the centre (or centers).
  • Theorem 8: A tangent to a circle is perpendicular to the radius through the point of contact.
  • Theorem 9: Lengths of two tangents drawn from an external point to a circle are equal.

SECTION – I (OBJECTIVE)

1. In a circle of radius 10 cm, the length of chord whose distance is 6 cm from the centre is:

  1. 4 cm
  2. 5 cm
  3. 8 cm
  4. 16 cm

2. If a chord of length 8 cm is situated at a distance of 3 cm from centre, then the diameter of circle is:

  1. 11cm
  2. 10cm
  3. 12cm
  4. 15cm

3. In the given circle ABCD, O is the centre and ∠BDC = 42°. Then ∠ACB is equal to:

  1. 48°
  2. 45°
  3. 42°
  4. 60°

Circle

4.In the given figure, ∠CAB = 80°, ∠ABC = 40°. The sum of ∠DAB + ∠ABD is equal to:

Circles

  1. 80°
  2. 100°
  3. 120°
  4. 140°

5. In the given figure, if C is the centre of the circle and ∠PQC = 25° and ∠PRC = 15° , then ∠QCR is equal to:

Circles

  1. 40°
  2. 60°
  3. 80°
  4. 120°

6. In a cyclic quadrilateral if ∠B - ∠D = 60°, then the smaller of the angles B and D is:

  1. 30°
  2. 45°
  3. 60°
  4. 75°

7. In the diagram two equal circles of radius 4 cm intersect each other such that each passes through the centre of the other. Find the length of the common chord.

  1. 2 √3 cm
  2. 4 √3 cm
  3. 4√3 cm
  4. 8cm

Circles

8. The length of a chord of a circle is equal to the radius of the circle. The angle which this chord subtends on the longer segment of the circle is equal to:

  1. 30°
  2. 45°
  3. 60°
  4. 90°

9. The length of the tangent drawn from a point 8 cm away from the centre of a circle of radius 6 cm is:

  1. √7 cm
  2. 2√7 cm
  3. 10 cm
  4. 5 cm

10. In a circle radius of 5 cm, AB and AC are two chords such that AB = AC = 6 cm. find the length of the chord BC.

  1. 9.6
  2. 4.8
  3. 10
  4. None of these

11. In figure, ∠ABC = 69° , ∠ACB = 31° , ∠BDC is:

  1. 80°
  2. 75°
  3. 90°
  4. None of these

Circles

12.Two parallel chords AB and CD, of lengths 6 cm and 8 cm respectively, are 1 cm apart. The radius of the circle is :

Circles

  1. 2.5 cm
  2. 4 cm
  3. 5 cm
  4. 5.5 cm

13.In the adjoining figure, x : y is equal to, where O is centre of circle?

Circles

  1. 1:1
  2. 2:1
  3. 3:2
  4. 1:4

14.The value of x in the given figure is:

Circles

  1. 30°
  2. 20°
  3. 10°
  4. 40°

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