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.
![8(8+x+5)=7(7+2x+1)](https://tex.z-dn.net/?f=8%288%2Bx%2B5%29%3D7%287%2B2x%2B1%29)
![8(x+13)=7(2x+8)](https://tex.z-dn.net/?f=8%28x%2B13%29%3D7%282x%2B8%29)
![8x+104=14x+56](https://tex.z-dn.net/?f=8x%2B104%3D14x%2B56)
![6x=48](https://tex.z-dn.net/?f=6x%3D48)
![x=8](https://tex.z-dn.net/?f=x%3D8)
Using this value, we can find the length of line segment MK.
![MK=x+5+8](https://tex.z-dn.net/?f=MK%3Dx%2B5%2B8)
![MK=8+5+8](https://tex.z-dn.net/?f=MK%3D8%2B5%2B8)
![MK=21](https://tex.z-dn.net/?f=MK%3D21)
Hope this helps!