10th class Mathematics, Chapter 9: Tangent and Angles of a Circle MCQs

1. Tangent is a line that touches the circumference of the circle at:

1. (A) many points
2. (B) three points
3. (C) two points
4. (D) one point ✓

2. _____ tangents can be drawn to a circle from a point outside the circle.

1. (A) one
2. (B) two ✓
3. (C) three
4. (D) many

3. _____ tangents can be drawn to a circle from the centre of the circle.

1. (A) zero ✓
2. (B) one
3. (C) two
4. (D) three

4. In a circle, radius and tangent are:

1. (A) parallel
2. (B) equal
3. (C) perpendicular ✓
4. (D) zero

5. An angle in a segment greater than a semicircle is _____ angle:

1. (A) an acute ✓
2. (B) right
3. (C) an obtuse
4. (D) straight

6. The angle subtended by the arc at the centre of the circle is called:

1. (A) acute angle
2. (B) central angle ✓
3. (C) right angle
4. (D) complete angle

7. What is the measure of an angle inscribed in a semi-circle?

1. (A) 45°
2. (B) 60°
3. (C) 90° ✓
4. (D) 120°

8. Any two angles in the same segment of the circle are:

1. (A) supplementary
2. (B) complementary
3. (C) equal ✓
4. (D) zero

9. Area of the sector of the circle =

1. (A) ½rθ
2. (B) 3/2 r²θ
3. (C) ½r²θ ✓
4. (D) 3/2 rθ

10. If r = 6 cm and θ = 2 radians, then the arc length is:

1. (A) 12 cm ✓
2. (B) 8 cm
3. (C) 6 cm
4. (D) 3 cm

11. A tangent to a circle meets the circle in:

1. (A) two points
2. (B) no point
3. (C) three points
4. (D) exactly one point ✓

12. The radius drawn to the point of contact of a tangent makes with the tangent an angle of:

1. (A) 180°
2. (B) 90° ✓
3. (C) 45°
4. (D) 60°

13. A line perpendicular to a radius at its outer end is a:

1. (A) diameter
2. (B) tangent ✓
3. (C) secant
4. (D) chord

14. The lengths of the two tangents from an external point to a circle are:

1. (A) double each other
2. (B) zero
3. (C) equal ✓
4. (D) unequal

15. The number of tangents that can be drawn to a circle from a point inside it is:

1. (A) infinite
2. (B) 0 ✓
3. (C) 1
4. (D) 2

16. The number of tangents at a given point of a circle is:

1. (A) 0
2. (B) infinite
3. (C) 1 ✓
4. (D) 2

17. From a point 5 cm from the centre of a circle of radius 3 cm, the length of the tangent is:

1. (A) 8 cm
2. (B) 2 cm
3. (C) √34 cm
4. (D) 4 cm ✓

18. If two circles touch externally, the distance between their centres is the _____ of their radii.

1. (A) sum ✓
2. (B) difference
3. (C) product
4. (D) ratio

19. If two circles touch internally, the distance between their centres is the _____ of their radii.

1. (A) sum
2. (B) product
3. (C) ratio
4. (D) difference ✓

20. Two circles of radii 3 cm and 5 cm touch externally. The distance between their centres is:

1. (A) 8 cm ✓
2. (B) 2 cm
3. (C) 15 cm
4. (D) 4 cm