Consider the circle
we have the intersecting chords theorem, which states that
[tex]a\cdot b=c\cdot d[/tex]
In our case we have a=x, b=12, c=6 and d=x+4. So we have
[tex]12\cdot x=6\cdot(x+4)[/tex]
distributing on the right side we get
[tex]12\cdot x=6x+6\cdot4=6x+24[/tex]
Subtracting 6x on both sides, we get
[tex]24=12x\text{ -6x=6x}[/tex]
Dividing boht sides by 6, we get
[tex]x=\frac{24}{6}=4[/tex]
So, the value of x is 4. Now we replace this value to find the length of each chord, so we have
x---->4
12---->12
x+4----->4+4=8
6----->6
