Multiple Choice Questions on AB is a line segment of length 2a with M as mid ndash point Semicircles are drawn on one side with A........... for CDS Exam Preparation

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Multiple Choice Questions

AB is a line segment of length 2a with M as mid ndash point Semicircles are drawn on one side with A...........

Quantitative Aptitude (CDS) Coordinate Geometry
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    AB is a line segment of length 2a, with M as mid–point. Semicircles are drawn on one side with AM, MB and AB as diameter as shown in the above figure. A circle with centre O and radius r is drawn such that this circle touches all the three semicircles. The value of r is

    \frac{2a}{3}

    Incorrect Answer

    \frac{a}{2}

    Incorrect Answer

    \frac{a}{3}

    Correct Answer

    \frac{a}{4}

    Incorrect Answer
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    Explanation:

    AB = 2a i.e., AL = LM = MN = NB =(a/2)
    Let OC = r
    In ΔOML, OM= a- r and OL = OP + PL = r + a / 2

    \therefore \left ( \frac{a}{2} \right )^{2}+( a - r)^{2} = \left ( r+\frac{a}{2} \right )^{2}

    On solving we get r = a / 3

    By: Munesh Kumari
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