# 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 -

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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