Answer:
x = 15
Step-by-step explanation:
The given diagram shows a circle with two intersecting chords.
To find the value of x, we can use the Intersecting Chords Theorem.
The Intersecting Chords Theorem states that when two chords intersect inside a circle, the product of the lengths of the segments of one chord is equal to the product of the lengths of the segments of the other chord.
In this case, the segments of one chord are 3 and x, and the segments of the other chord are 9 and 5, so:
[tex]3 \cdot x = 9 \cdot 5[/tex]
Simplify:
[tex]3x=45[/tex]
Now, divide both sides by 3 to isolate x:
[tex]\dfrac{3x}{3}=\dfrac{45}{3}\\\\\\x=15[/tex]
Therefore, the value of x is:
[tex]\LARGE\boxed{\boxed{x=15}}[/tex]
