10th class Mathematics, Chapter 10: Practical Geometry of Circles MCQs

1. In the figure, a line ABC touching the circle at B is:

1. (A) a chord
2. (B) an arc
3. (C) a tangent ✓
4. (D) a secant

2. There are _____ types of arcs.

1. (A) 2 ✓
2. (B) 3
3. (C) 4
4. (D) 5

3. The right bisector of a chord of a circle always passes through the:

1. (A) diameter
2. (B) non-collinear points
3. (C) radius
4. (D) centre ✓

4. A circle has only one:

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

5. The point where two tangents meet outside a circle forms:

1. (A) a semicircle
2. (B) a diameter
3. (C) a radius
4. (D) an angle ✓

6. Two equal tangents from a point to a circle can be drawn when the point is _____ the circle.

1. (A) on
2. (B) inside
3. (C) outside ✓
4. (D) at centre of

7. Tangents drawn from a single external point to a circle are:

1. (A) unequal in length
2. (B) perpendicular to each other
3. (C) equal in length ✓
4. (D) inside the circle

8. At least how many chords are needed to locate the centre of the circle?

1. (A) 1
2. (B) 2 ✓
3. (C) 3
4. (D) 4

9. To draw a tangent at the middle point of an arc, the first step is to:

1. (A) join endpoints of an arc ✓
2. (B) draw radius
3. (C) draw a line perpendicular to chord
4. (D) draw an angle

10. The angle between the radius and a tangent at the point of contact is:

1. (A) 30°
2. (B) 60°
3. (C) 90° ✓
4. (D) 120°

11. The centre of a circle is found as the point of intersection of the:

1. (A) two radii of the same length
2. (B) two parallel chords
3. (C) right bisectors of two chords ✓
4. (D) two tangents

12. To draw a circle through three non-collinear points A, B and C, the centre is the intersection of the right bisectors of:

1. (A) the radius and AB
2. (B) AC and the angle bisector at B
3. (C) AB and BC ✓
4. (D) AB and the tangent at A

13. The three points through which one and only one circle passes must be:

1. (A) on the same chord
2. (B) non-collinear ✓
3. (C) collinear
4. (D) equidistant

14. To complete a circle from a given arc by finding its centre, we need at least _____ points on the arc.

1. (A) 3 ✓
2. (B) 2
3. (C) 1
4. (D) 4

15. To complete a circle without finding the centre we take two equal chords AB and BC of the arc and construct equal:

1. (A) arcs only
2. (B) diameters
3. (C) tangents
4. (D) angles ✓

16. The tangent at the midpoint P of an arc APB is parallel to the:

1. (A) chord AB ✓
2. (B) radius OP
3. (C) right bisector of AB
4. (D) diameter through A

17. A tangent at a point P of a circle with centre D is drawn:

1. (A) parallel to DP
2. (B) at 45° to DP
3. (C) through D
4. (D) perpendicular to DP ✓

18. To draw a tangent from an outside point P to a circle with centre O, a semi-circle is drawn on OP as:

1. (A) radius
2. (B) tangent
3. (C) chord of the circle
4. (D) diameter ✓

19. The semi-circle on OP (O the centre, P an outside point) cuts the given circle at T. Then ∠OTP is:

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

20. The angle between the radii to the points of contact of two tangents meeting at 30° is:

1. (A) 150° ✓
2. (B) 30°
3. (C) 60°
4. (D) 90°