Geometry

A circle is divided into two parts by a chord, 3cm a wat from the center. Find the area of the smaller part if the circle has an area of 201cm squared.

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  1. Did you make your sketch?
    Complete the central triangle with the chord as its base
    let the central angle be 2Ø

    area of whole circle = πr^2 = 201
    r = √(201/π)

    cosØ = 3/√(201/π) = ....
    Ø = appr ....
    2Ø = .....

    we can find the area of the central triangle:
    = (1/2)(r)(r)sin(2Ø) = ......

    Also the area of the sector using ratios:
    2Ø/360° = sector/210
    sector = 210Ø/180

    subtract the triangle area from the sector area and you have the segment area

    I will leave all that calculation stuff up to you

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