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What is the area of the minor segment cut off a circle of radius 10 cm by a chord of length 12 cm?

Could you please show me the working out for this question?

The answer in the textbook is 16 sq cm.


  • Maths -

    Make a sketch showing the chord of 12 and the the two radii of 10.
    I see an isosceles triangle. Draw an altitude from the centre to that chord, making two congruent right-angled triangles.
    let the height be x, then x^2 + 6^2 = 10^2
    x^2 = 100-36 = 64
    x = √64 = 8
    So the area of the large triangle, 10,10,12 is
    (1/2) (12)(8) = 48 cm^2

    We have to find the central angle of the sector.
    Let each angle at the centre of the right-angled triangles be Ø
    sinØ = 6/10 = .6
    Ø = 36.87‡
    and the central angle is 2Ø = 73.74°

    area of whole circle = π(10)^2 = 100π
    area of sector/100π = 73.74/360
    area of sector = 64.35 cm^2

    sooo, the segment is 64.35 - 48 = 16.35 cm^2

    (I carried all decimals my calculator could hold and only rounded off the final answer.)

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