Hello!
This is a problem about relating circle theorems to line lengths.
We can first see that both line segment MK and CM are secants within the circle that come from a common point K.
This means that the Intersecting Secant Theorem applies here.
The Intersecting Secant Theorem states that if two secants are formed from a common point outside the circle, the length of each secant multiplied by the length of its corresponding external secant are equivalent.
We can set up the following equation.
[tex]8(8+x+5)=7(7+2x+1)[/tex]
[tex]8(x+13)=7(2x+8)[/tex]
[tex]8x+104=14x+56[/tex]
[tex]6x=48[/tex]
[tex]x=8[/tex]
Using this value, we can find the length of line segment MK.
[tex]MK=x+5+8[/tex]
[tex]MK=8+5+8[/tex]
[tex]MK=21[/tex]
Hope this helps!
