Ncert Solutions For Class 10 Maths

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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:

(A) 4 cm (B) 5 cm (C) 8 cm (D) 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:

(A) 11cm (B)10cm (C) 12cm (D) 15cm

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

(A) 48°
(B) 45°
(C) 42°
(D) 60°

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

(A) 80° ∠PQC = 25° and
(B) 100°
(C) 120°
(D) 140°
5. In the given figure, if C is the centre of the circle and
∠PRC = 15° , then ∠QCR is equal to:

(A) 40°
(B) (B) 60°
(C) (C) 80°
(D) (D) 120°

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

(A) 30° (B) 45° (C) 60° (D) 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.

(A) 2√3cm

(B) 4√3cm

(C) 4√2 cm

(D) 8 cm

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:

(A) 30° (B) 45° (C) 60° (D) 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:

(A)√7cm (B) 2√7cm (C) 10 cm (D) 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.

(A) 9.6 (B) 4.8 (C) 10 (D) None of these

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

(A) 80°
(B) 75°
(C) 90°
(D) None of these
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 :

(A) 2.5 cm
(B) 4 cm
(C) 5 cm
(D) 5.5 cm
13. In the adjoining figure, x : y is equal to, where O is centre of circle?

(A)1:1
(B) 2:1
(C) 3:2
(D) 1:4

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

(A) 30°
(B) 20°
(C) 10°
(D) 40°

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Answers 2) B 3) A 4) C 5) C 6) C 7) B
1) D 9) B 10) A 11) A 12) C 13) A 14) C
8) A

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