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Largest square in a circle or largest circle in a square: areas

This type of question, asked 4 times: CDS 1 2018, CDS 1 2019, CDS 1 2020, CDS 2 2025. All 4 questions below, oldest first.

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  1. Question 1

    CDS 1 2018

    91
    What is the area of the largest circular disc cut from a square of side 2π\dfrac{2}{\sqrt{\pi}} units ?

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  2. Question 2

    CDS 1 2019

    52
    A square is drawn such that its vertices are lying on a circle of radius 201 mm. What is the ratio of area of circle to that of square ?

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  3. Question 3

    CDS 1 2020

    86
    What is the area of the largest square plate cut from a circular disk of radius one unit ?

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  4. Question 4

    CDS 2 2025

    80
    Let the area of the largest possible square inscribed in a circle of unit radius be xx. Let the area of the largest possible circle inscribed in a square of unit side length be yy. What is the relation between xx and yy?

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