Answer:
The length of the radius of the circle K is [tex]17\ units[/tex]
Step-by-step explanation:
we know that
The triangle CDE is a right triangle with the 90 degree angle at point E
so
Applying the Pythagoras Theorem
Find the length of CD (diameter of the circle K)
[tex]CD^{2}=CE^{2}+DE^{2}[/tex]
substitute the values
[tex]CD^{2}=16^{2}+30^{2}[/tex]
[tex]CD^{2}=1,156[/tex]
[tex]CD=34\ units[/tex]
Find the radius
Remember that the radius is half the diameter
so
[tex]r=34/2=17\ units[/tex]
