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Chord, its distance from the centre and the radius: r^2 = d^2 + (c/2)^2

This type of question, asked 5 times: CDS 2 2016, CDS 1 2022, CDS 2 2023, CDS 2 2025, CDS 2 2026. All 5 questions below, oldest first.

Try each one first, then open its answer.

  1. Question 1

    CDS 2 2016

    48
    In a circle of radius 3 units, a diameter ABAB intersects a chord of length 2 units perpendicularly at PP. If AP>BPAP > BP, then what is the ratio of APAP to BPBP ?

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  2. Question 2

    CDS 1 2022

    62
    A circle of radius 25 cm has a chord of length 48 cm. What is the length of the perpendicular drawn from the centre of the circle to the chord?

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  3. Question 3

    CDS 2 2023

    62
    The arch of a bridge is in the form of an arc of a circle. If the span of the bridge is 40 m and height in the middle is 8 m, then what is the radius of curvature of the bridge ?

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  4. Question 4

    CDS 2 2025

    65
    In a circle of radius 14 cm, APBAPB is a shorter arc and PP is the midpoint of the arc. Let CC be the midpoint of the chord ABAB and PC=7PC = 7 cm. What is the length of the chord APAP ?

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  5. Question 5

    CDS 2 2026

    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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