The given chord is in red.  The radius in r.  We want to find r. 



Draw a perpendicular line from the center to the red chord, which
divides the 18cm chord into two 9cm line segments, and divides
the 100° angle into two 50° angles:


Looking only at the upper right triangle:

9cm is the side opposite the 50° angle
and r is the hypotenuse:

The trig ratio that involves the opposite and the hypotenuse is the
sine.





Multiply both sides by r:





Divide both sides by sin(50°)



cm. 

Edwin