CIRCLE (CDS)

Total Questions: 46

1. A line segment AB is the diameter of a circle with centre at O having radius 6.5 cm. Point P is in the plane of the circle such that AP = x and BP = y. In which one of the following cases the point P does not lie on the circle?

Correct Answer: (a) x = 6.5cm and y = 6.5cm
Solution:


2. Consider a trapezium ABCD, in which AB is parallel to CD and AD is perpendicular to AB. If the trapezium has an incircle which touches AB at E and CD CD at F, where EB = 25 cm and FC = 16 cm, then what is the diameter of the circle?

Correct Answer: (d) 40 cm
Solution:


3. If the lengths of two parallel chords in a circle of radius 10 cm are 12 cm and 16 cm, then what is the distance between these two chords?

Correct Answer: (b) 2 cm or 14 cm
Solution:Radius of circle = 10 cm



4. In a circle of radius 8 cm, AB and AC are two chords such that AB = AC = 12 cm. What is the length of chord BC ?

Correct Answer: (d) 6 √7 cm
Solution:In a circle, Radius = 8 cm, AB = AC = 12 cm, AB and AC are chords of circle.


5. Two equal circles intersect such that each passes through the centre of the other. If the length of the common chord of the circles is 10 √3 cm, then what is the diameter of the circle?

Correct Answer: (c) 20 cm
Solution:Two equal circles intersect such that each passes through the centre of the other.


6. Consider the following statements.

I. The number of circles that can be drawn through three non-collinear points is infinity. II. Angle formed in minor segment of a circle is acute.

Which of the above statements is/are correct?

Correct Answer: (d) Neither I nor II
Solution:I. Only one circle can be drawn from three non-collinear points.
II. (i) Angle formed in minor segment of a circle is obtuse.
(ii) Angle formed in major segment of a circle is acute.
Then, Option (d) is correct.

7. The chord of a circle is √3 times its radius. The angle subtended by this chord at the minor arc is k times the angle subtended at the major arc. What is the value of k ?

Correct Answer: (b) 2
Solution:


8. If a point P moves such that the sum of the squares of its distances from two fixed points A and B is a constant, then the locus of the point P is

Correct Answer: (b) a circle
Solution:

9. In the figure given below, the radius of the circle is 6 cm and AT = 4 cm. The length of tangent PT is

Correct Answer: (b) 8 cm
Solution:Here, OP = 6 cm

10. In the figure given below, what is ∠BCD equal to?

Correct Answer: (c) 80º
Solution:∠CAD = ∠CBD