Answer:
4 units
Step-by-step explanation:
<u><em>The complete question is</em></u>
BD and AC are chords that intersect at point Y. A circle is shown. Chords B D and A C intersect at point Y. The length of B Y is 3, the length of Y D is 8, the length of A Y is x, and the length of Y C is 6. What is the length of line segment AY?
<u><em>The picture of the question in the attached figure</em></u>
we know that
The <u><em>Intersecting Chord Theorem</em></u> states that: When two chords intersect each other inside a circle,the products of their segments are equal.
do
In this problem

substitute the given values

solve for x

therefore
The length of segment AY is 4 units
The maximum product is 42. Numbers 6 and 7 yield this product.
Answer:
x = 3
Step-by-step explanation:
Once again we want to use the relationship stated earlier
Where A * B = C * D
Once again imagine that the segments in the given problem have letters
A = x
B = 12
C = x + 1
D = 9
Now we create an equation using the relationship
12 * x = 9(x+1)
now we solve using basic algebra
step 1 distribute the 9 to the x and the 1
9 * x = 9x
9 * 1 = 9
now we have 12x = 9x + 9
step 2 subtract 9x from each side
12x - 9x = 3x
9x - 9x cancels out
now we have 3x = 9
step 3 divide each side by 3
3x/3=x
9/3=3
we're left with x = 3