Answer:
The value of EK is [tex]6\ units[/tex]
Step-by-step explanation:
we know that
Applying The Intersecting Secant Theorem
[tex]SJ*SI=SK*SE[/tex]
we have
[tex]SJ=SI+IJ=8+12=20\ units[/tex]
[tex]SI=8\ units[/tex]
[tex]SK=SE+EK=(10+EK)\ units[/tex]
[tex]SE=10\ units[/tex]
substitute the values
[tex]20*8=(10+EK)*10[/tex]
Simplify
[tex]2*8=(10+EK)*1[/tex]
[tex]16=10+EK[/tex]
[tex]EK=16-10=6\ units[/tex]
