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Math Help - Angle Measurement

  1. #1
    Junior Member
    Joined
    Jul 2009
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    35

    Angle Measurement

    Can someone help me in this problem? I try it but I cannot get the right answer


    Three circles with radius 1,2, and 3 ft are extremely tangent to one another. Find the area of the sector of the circle of radius 1 that is cut off by the line segments
    joining the center of that circle to the centers of the other two circles.



    I think this is the figure of that one
    Attached Thumbnails Attached Thumbnails Angle Measurement-lop.jpg  
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  2. #2
    Senior Member nikhil's Avatar
    Joined
    Jun 2008
    Posts
    292

    Lightbulb its easy

    let centre of circle with radius 1 ft= A
    let centre of circle with radius 2 ft= B
    let centre of circle with radius 3 ft= c
    join ABC
    so AB=3 ft,BC=5ft,CA=4 ft
    it clearly shows that ABC is a right angle triangle with angle CAB=90 degrees.
    now we may calculate area of sector of circle with centre A
    since angle A is 90 degrees therefor
    area of sector = (1/4) area of circle
    =(1/4)(pi (1)^2)
    =pi/4 square ft
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