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Circles

CDS Maths. Try each one first, then open its answer.

Top 10 CDS PYQs to practise first

The questions and kinds of question asked most often come first. Each one says how often and in which papers.

  1. Question 1

    This type asked 5 times: CDS 2 2016, CDS 1 2022, CDS 2 2023, CDS 2 2025, CDS 2 2026. This one: CDS 2 2026 See all 5 of this type

    57
    The chord of a circle is 20 cm and the height of the minor segment is 5 cm. What is the diameter of the circle ?

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  2. Question 2

    This type asked 5 times: CDS 2 2016, CDS 1 2020, CDS 2 2021, CDS 2 2022, CDS 1 2026. This one: CDS 1 2026 See all 5 of this type

    75
    A Question is given followed by two Statements I and II. Consider the Question and the Statements and mark the correct option. Question : Two circles with radii p, q (p>q)(p > q) in cm touch externally, where p, q are natural numbers and each greater than 1. What is the value of (p−q)(p - q) ? Statement-I : The sum of their areas is 130π130\pi cm2\text{cm}^2 Statement-II : The distance between the centres of the two circles is 14 cm Which one of the following is correct in respect of the above Question and the Statements ?

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  3. Question 3

    This type asked 5 times: CDS 1 2017, CDS 2 2017, CDS 2 2019, CDS 2 2023, CDS 1 2026. This one: CDS 1 2026 See all 5 of this type

    65
    Let O be the centre of a circle. Let the chords AB = 10 cm and CD = 24 cm be two parallel chords of the circle. The two chords are on opposite side of the centre and the distance between them is 17 cm. Let P be the midpoint of AB and Q be the midpoint of CD. Further, the points O and A, the points O and C, the points A and C are joined. Which of the statements given below is/are correct ? I. Area of triangle OAP is equal to area of triangle OCQ. II. Area of triangle OAC is equal to 102102 cm2\text{cm}^2. Select the answer using the code given below :

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  4. Question 4

    Asked 3 times: CDS 2 2016*, CDS 2 2021*, CDS 2 2022 (* = numbers or wording changed that year) See all 3 times it was asked

    88
    Two circles touch externally. The sum of their areas is 89π89\pi square cm and the distance between their centres is 13 cm. What is the difference in their radii ?

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  5. Question 5

    This type asked 3 times: CDS 1 2021, CDS 1 2025, CDS 2 2025. This one: CDS 2 2025 See all 3 of this type

    87
    A Question is given followed by two Statements I and II. Consider the Question and the Statements. Question : AB and CD are chords of a circle intersecting at P. If AP×PB=48AP \times PB = 48 square units, then what is CP×PDCP \times PD equal to? Statement-I : AP=8AP = 8 units Statement-II : CP=10CP = 10 units Which one of the following is correct in respect of the above Question and the Statements?

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  6. Question 6 (case study, 2 parts)

    This type asked 3 times: CDS 2 2017, CDS 1 2018, CDS 1 2025. This one: CDS 1 2025 See all 3 of this type

    Consider the following for the next two (02) items that follow : A circle M of radius 8 cm touches externally with another circle N of radius 16 cm. Let P, Q be the points where the common tangent touches the circles M and N respectively.
    55
    What is the length of the common tangent PQ ?

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    56
    If U, V are the centres of the circles M and N respectively, then what is the area of the quadrilateral formed by the points P, Q, V and U ?

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  7. Question 7

    Asked 2 times: CDS 1 2018*, CDS 1 2026 (* = numbers or wording changed that year) See all 2 times it was asked

    63
    A triangle PQR is inscribed in a circle with its centre at O. A tangent PT is drawn at P such that ∠QPT=36∘\angle QPT = 36^\circ. What is ∠POQ\angle POQ equal to ?

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  8. Question 8

    Asked 2 times: CDS 2 2019*, CDS 1 2020 (* = numbers or wording changed that year) See all 2 times it was asked

    70
    In a circle of radius 5 cm, ABAB and ACAC are two chords such that AB=AC=8AB = AC = 8 cm. What is the length of chord BCBC ?

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  9. Question 9

    Asked 2 times: CDS 1 2017*, CDS 2 2019 (* = numbers or wording changed that year) See all 2 times it was asked

    74
    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 ?

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  10. Question 10

    This type asked 2 times: CDS 1 2019, CDS 2 2026. This one: CDS 2 2026 See all 2 of this type

    65
    A Question is given followed by two Statements I and II. Consider the Question and the Statements and mark the correct option. Question : ABC is a triangle inscribed in a semi-circle such that AC coincides with the diameter of the semi-circle. Let P be any point on the arc of the semi-circle. What is AP2+CP2+AC2AP^2 + CP^2 + AC^2 equal to ? Statement I : The radius of the circle is 5 cm. Statement II : AB = 6 cm and BC = 8 cm. Which one of the following is correct in respect of the above Question and Statements ?

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