NCERT Exemplar Problems – Class 10 Mathematics
Chapter 9: Circles
Multiple Choice Questions (Exercise 9.1) with Correct Answers
Note: In the NCERT Exemplar, Chapter 9 is Circles (Applications of Trigonometry are covered under Chapter 8).
Source: NCERT Exemplar Problems Class 10 Mathematics (Official Answer Key)
1. If radii of two concentric circles are 4 cm and 5 cm, then the length of each chord of one circle which is tangent to the other circle is
(A) 3 cm (B) 6 cm (C) 9 cm (D) 1 cm
Correct Answer: (B)
2. In Fig. 9.3, if \(\angle AOB = 125^\circ\), then \(\angle COD\) is equal to
(A) \(62.5^\circ\) (B) \(45^\circ\) (C) \(35^\circ\) (D) \(55^\circ\)
Note: Refer to Fig. 9.3 in the original book.
Correct Answer: (D)
3. In Fig. 9.4, AB is a chord of the circle and AOC is its diameter such that \(\angle ACB = 50^\circ\). If AT is the tangent to the circle at the point A, then \(\angle BAT\) is equal to
(A) \(65^\circ\) (B) \(60^\circ\) (C) \(50^\circ\) (D) \(40^\circ\)
Note: Refer to Fig. 9.4 in the original book.
Correct Answer: (C)
4. From a point P which is at a distance of 13 cm from the centre O of a circle of radius 5 cm, the pair of tangents PQ and PR to the circle are drawn. Then the area of the quadrilateral PQOR is
(A) \(60\,\mathrm{cm}^{2}\) (B) \(65\,\mathrm{cm}^{2}\) (C) \(30\,\mathrm{cm}^{2}\) (D) \(32.5\,\mathrm{cm}^{2}\)
Correct Answer: (A)
5. At one end A of a diameter AB of a circle of radius 5 cm, tangent XAY is drawn to the circle. The length of the chord CD parallel to XY and at a distance 8 cm from A is
(A) 4 cm (B) 5 cm (C) 6 cm (D) 8 cm
Correct Answer: (D)
6. In Fig. 9.5, AT is a tangent to the circle with centre O such that OT = 4 cm and \(\angle OTA = 30^\circ\). Then AT is equal to
(A) 4 cm (B) 2 cm (C) \(2\sqrt{3}\) cm (D) \(4\sqrt{3}\) cm
Note: Refer to Fig. 9.5 in the original book.
Correct Answer: (C)
7. In Fig. 9.6, if O is the centre of a circle, PQ is a chord and the tangent PR at P makes an angle of \(50^\circ\) with PQ, then \(\angle POQ\) is equal to
(A) \(100^\circ\) (B) \(80^\circ\) (C) \(90^\circ\) (D) \(75^\circ\)
Note: Refer to Fig. 9.6 in the original book.
Correct Answer: (A)
8. In Fig. 9.7, if PA and PB are tangents to the circle with centre O such that \(\angle APB = 50^\circ\), then \(\angle OAB\) is equal to
(A) \(25^\circ\) (B) \(30^\circ\) (C) \(40^\circ\) (D) \(50^\circ\)
Note: Refer to Fig. 9.7 in the original book.
Correct Answer: (A)
9. If two tangents inclined at an angle \(60^\circ\) are drawn to a circle of radius 3 cm, then length of each tangent is equal to
(A) \(\dfrac{3\sqrt{3}}{2}\) cm (B) 6 cm (C) 3 cm (D) \(3\sqrt{3}\) cm
Correct Answer: (D)
10. In Fig. 9.8, if PQR is the tangent to a circle at Q whose centre is O, AB is a chord parallel to PR and \(\angle BQR = 70^\circ\), then \(\angle AQB\) is equal to
(A) \(20^\circ\) (B) \(40^\circ\) (C) \(35^\circ\) (D) \(45^\circ\)
Note: Refer to Fig. 9.8 in the original book.
Correct Answer: (B)
Answers taken from the official NCERT Exemplar answer key.