Tiny Segmental Area

Discussion in 'Online Games & Puzzles' started by Thyagarajan, Oct 29, 2022.

  1. Thyagarajan

    Thyagarajan Finest Post Winner

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    How do we get the area of of tiny white segment in red circle bounded by blue arc and red straight line.
    The black dot coordinates are as shown in brackets in fig above.​
     
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  2. hrastro

    hrastro Finest Post Winner

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    On the first look, I thought I have to integrate the area under curve - so calculus would be the only way... but on further thought, if we could consider that the two segments on either side of the y-axis (Line ABC) are equal, it is now a simple matter of understanding circles and trigonometry and co-ordinate plane.

    So, I named the points A,B,C,D and angle x as shown below. We need to find the area of the green portion. The answer is explained below - we get answer as [pi/3 - sqrt(3)/2] units...
    Please do let me know if there is anything wrong or if something needs more explanation
    Keep smiling
    HR

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  3. Thyagarajan

    Thyagarajan Finest Post Winner

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    Delighted. Full Marks.
    Regards.
     
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