CIRCLE (CDS)

Total Questions: 46

21. In the figure given below, D is the diameter of each circle. What is the diameter of the shaded circle?

Correct Answer: (a) D(√2 - 1)
Solution:

22. ABCDA is a con-cyclic quadrilateral of a circle ABCD with radius r and centre at O. If AB is the diameter and CD is parallel and half of AB and if the circle completes one rotation about the centre O, then the locus of the middle point of CD is a circle of radius.

Correct Answer: (d) √3r/2
Solution:

23. In a circle of radius 3 units, a diameter AB intersects a chord of length 2 units perpendicular at P. If AP BP > , then what is the ratio of AP to BP?

Correct Answer: (b)
Solution:


24. If a quadrilateral has an inscribed circle, then the sum of a pair of opposite sides equals

Correct Answer: (b) sum of the other pair of opposite sides
Solution:

25. If two tangents inclined at an angle 60° are drawn to a circle of radius 3 cm, then what is the length of each tangent?

Correct Answer: (a) 3√3 cm
Solution:

26. If a square of side x and an equilateral triangle of side y are inscribed in a circle, then what is the ratio of x to y?

Correct Answer: (a)
Solution:

27. A pole stands vertically inside a triangular park ABC. If the angle of elevation of the top of the pole from each corner of the park is same, then in the triangle ABC, the foot of the pole is at the

Correct Answer: (b) circumcentre
Solution:

28. Consider a circle with centre at O and radius 7 cm. Let QR be a chord of length 2 cm and let P be the mid-point of QR. Let CD be another chord of this circle passing through P such that ∠CPQ is acute. If M is the midpoint of CD and MP = √24 cm, then which of the following statements are correct ?

Correct Answer: (a) I and II
Solution:


29. Consider a circle with centre at C. Let OP, OQ denote respectively the tangents to the circle drawn from a point O outside the circle. Let R be a point on OP and S be a point on OQ such that OR × SQ = OS × RP. Which of the following statements is/are correct?

I. If X is the circle with centre at O and radius OR and Y is the circle with centre at O and radius OS, then X = Y.
II. ∠POC + ∠QCO = 90°

Select the correct answer using the codes given below.

Correct Answer: (c) Both I and II
Solution:

30. Suppose chords AB and CD of a circle intersect at a point P inside the circle. Two right angled ∆A′P′B′ and ∆C′Q′D′ are formed as shown in the figures below such that A′P′ = AP, B′P′ = BP, C′Q′ = CP, D′Q′ = DP and ∠A′P′B′ = 90° = ∠C′Q′D′ .

Which of the following statements are not correct?
I. ∆A′ P′ B′ and ∆C′ Q′ D′ are similar triangles but need not be congruent.
II. ∆A′ P′ B′ and ∆C′ Q′ D′ are congruent triangles.
III. ∆A′ P′ B′  and ∆C′ Q′ D′ are triangles of same area.
IV. ∆A′ P′ B′  and ∆C′ Q′ D′ are triangles of same perimeter.

Select the correct answer using the codes given below.

Correct Answer: (b) I and III
Solution: