To find the value of x in the figure with the circle and two chords, we can use the property that when two chords intersect inside a circle, the products of their segments are equal.
In this case, we can set up the following equation:
(8)(12) = x(x+12)
Solve for x:
96 = x^2 + 12x
x^2 + 12x - 96 = 0
Now, we can factor or use the quadratic formula to solve for x. The factors of -96 that add up to 12 are 16 and -6, so:
(x + 16)(x - 6) = 0
x = -16 or x = 6
Since x must be a positive value, x = 6.
Therefore, the value of x is 6.
A circle with two chords is shown below in the figure find the value of x
8
12
X+12
1 answer