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    What is the area of the largest square that is inscribed in a semicircle of radius 10 cm?
    Question

    What is the area of the largest square that is inscribed in a semicircle of radius 10 cm?

    A.

    70 cm²

    B.

    90 cm²

    C.

    80 cm²

    D.

    120 cm²

    Correct option is C

    Given:
    The radius of the semicircle r=10r = 10r=10 cm.
    Concept Used:
    The largest square inscribed in a semicircle will have one of its sides along the diameter of the semicircle, and the opposite two corners will touch the arc of the semicircle.
    Formula Used: 
    Area of square = a2a^2  
    Pythagoras theorem;  
    (Hypotenuse)2=(Perpendicular)2+(Base)2\text{(Hypotenuse)}^2 = \text{(Perpendicular)}^2 + \text{(Base)}^2 ​
    Solution:

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