Point C is the center of the circle. Arc AB measures 5x + 2. Angle ACB measures 3x + 14. Find the value of x.
To find the value of x, we can use the fact that the measure of an inscribed angle in a circle is equal to half the measure of its intercepted arc.
Given that Arc AB measures 5x + 2 and Angle ACB measures 3x + 14, we can set up the equation:
(3x + 14) = (1/2) * (5x + 2)
Now, let's solve for x:
Multiply both sides of the equation by 2 to eliminate the fraction:
2(3x + 14) = 5x + 2
Simplify the left side of the equation:
6x + 28 = 5x + 2
Subtract 5x from both sides:
6x - 5x + 28 = 2
Combine like terms:
x + 28 = 2
Subtract 28 from both sides:
x = 2 - 28
Simplify:
x = -26
Therefore, the value of x is -26.
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