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

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Multiple Choice Questions

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

Quantitative Aptitude (CDS) Mensuration 2D
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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 0 and radius r is drawn such that this circle touches all the three semicircles. The value of r is

    2a/3

    Incorrect Answer

    a/2

    Incorrect Answer

    a/3

    Correct Answer

    a/4

    Incorrect Answer
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    Explanation:

    AM=MB=2a/a=a

    P and Q are the centres of the circles with diameters AM and BM, respectively.
    PM=QM=a/2 ,OQ=r+a/2 and OM=a−r

    In right ΔOMQ
    (r+a/2)2=(a−r)2+(a/2)2

    =r2+a2/4+ar

    =a2+r2−2ar+a2/4

    ⇒3ar=a2

    ⇒r=a/3

    By: Munesh Kumari
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