Answer:
The length of the radius of circle is 16.25 cm
Step-by-step explanation:
we know that
If CD is tangent to circle A at point D
then
the segment CD is perpendicular to the radius AD
and
ACD is a right triangle
so
Applying the Pythagorean Theorem
[tex]AC^2=AD^2+CD^2[/tex]
we have
[tex]AC=AE+CE=(r+8)\ cm\\AD=r\ cm\\CD=18\ cm[/tex]
substitute
[tex](r+8)^2=r^2+18^2[/tex]
solve for r
[tex]r^2+16r+64=r^2+324\\16r=324-64\\16r=260\\r=16.25\ cm[/tex]
