geometry

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Point C is the center of the circle. Arc AB measures 5x + 2. Angle ACB measures 3x + 14. Find the value of x.

  • geometry -

    arc = radius * angle
    5x+2 = r * (3x+14)

    You still need to know the radius. If not, then

    5x+2 = 3rx + 14r
    5x-3rx = 14r-2

    x = (14r-2)/(5-3r)

    Keeping the same angle, a larger circle generates a longer arc.

    If r=1, then x = 6
    If r = 2, x = -12

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