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Circle inscribed in an equilateral triangle: inradius = side / (2 root 3)

This type of question, asked 4 times: CDS 2 2018, CDS 2 2022, CDS 1 2025, CDS 1 2026. All 4 questions below, oldest first.

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  1. Question 1

    CDS 2 2018

    72
    A circle is inscribed in an equilateral triangle of side of length ll. The area of any square inscribed in the circle is

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  2. Question 2

    CDS 2 2022

    94
    In an equilateral triangle of side 232\sqrt{3} cm, a circle is inscribed touching the sides. What is the area of the remaining portion of the triangle ?

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  3. Question 3

    CDS 1 2025

    73
    A circle is inscribed in an equilateral triangle. The radius of the circle is 2 cm. What is the area of the triangle ?

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  4. Question 4

    CDS 1 2026

    71
    A Question is given followed by two Statements I and II. Consider the Question and the Statements and mark the correct option. Question : A circle is inscribed in the equilateral triangle Δ\Delta. What is the radius of the circle ? Statement-I : Area of Δ\Delta is equal to 16316\sqrt{3} cm2\text{cm}^2. Statement-II : Perimeter of Δ\Delta is 24 cm. Which one of the following is correct in respect of the above Question and the Statements ?

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