CIRCLE (CDS)

Total Questions: 46

31. A tangent is drawn from an external point O to a circle of radius 3 units at P such that OP = 4 units. If C is the centre of the circle, then the sine of ∠COP is

Correct Answer: (c) 3/5
Solution:

32. In a circle of radius 2 units, a diameter AB intersects a chord of length 2 units perpendicularly at P. If AP BP > , then AP is equal to

Correct Answer: (b) (2 + √3) units
Solution:

33. The two adjacent sides of a cyclic quadrilateral are 2 cm and 5 cm and the angle between them is 60°. If the third side is 3 cm, then the fourth side is of length

Correct Answer: (a) 2 cm
Solution:


34. Simplify the question


From an external point P, tangents PA and PB are drawn to the circle as shown in the above figure.
CD is the tangent to the circle at E. If AP = 16 cm, then the perimeter of the ∆PCD is equal to

Correct Answer: (d) 32 cm
Solution:

35. Chord CD intersects the diameter AB of a circle at right angle at a point P in the ratio 1:2. If diameter of circle is d, then CD is equal to

Correct Answer: (c)
Solution:

36. AD is the diameter of a circle and AB is a chord. If AD = 34 cm, AB = 30 cm, then the distance of AB from the centre of the circle is

Correct Answer: (d) 8 cm
Solution:

37. If the angle between the radii of a circle is 130°, then the angle between the tangents at the ends of the radii is

Correct Answer: (c) 50°
Solution:

38. Out of two concentric circles, the diameter of the outer circle is 26 cm and the chord MN of length 24 cm is tangent to the inner circle. The radius of the inner circle is

Correct Answer: (a) 5 cm
Solution:

39. A ∆ABC is inscribed in a circle. If sum of the squares of sides of the triangle is equal to twice the square of the diameter, then sin² A + sin² B + sin² C is equal to

Correct Answer: (a) 2
Solution:

40. If the chord of an arc of a circle is of length x, the height of the arc is y and the radius of the circle is z. Then, which one of the following is correct?

Correct Answer: (d) 4y(2z - y) = x²
Solution: