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March 30, 2017

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In a circle , the radius is 68 units and a chord of the circle is 120 units.
Part A)How far is the chord from the center?
Part B)Find the measure of the arc created by the chord.

  • Math - ,

    A) Let x be the distance of the chord from the center. Draw a line from the center of the chord to the center of the circle. This forms a right triangle with a radius and half the chord.
    x^2 + 60^2 = r^2 = 4624
    x^2 = 1024
    x = 32

    B) The angle subtended by the chord is 2 arcsin 60/68 = 123.85 degrees = 2.162 radians
    Multiply that by the radius to get the arc length, 147.0 units.. a bit longer than the chord length, as you would expect.

  • Math - ,

    your mom

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