Question 879405
<pre>

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

{{{drawing(300,300,-1.5,1.5,-1.5,1.5,

circle(0,0,1), green(line(0,0,cos(50*pi/180),sin(50*pi/180)),
 line(0,0,cos(50*pi/180),-sin(50*pi/180))),locate(.1,.08,"100°"),
locate(.67,.08,18cm),locate(.2,.5,r),
red(line(cos(50*pi/180),sin(50*pi/180),cos(50*pi/180),-sin(50*pi/180)))


  )}}}

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:
{{{drawing(300,300,-1.5,1.5,-1.5,1.5,

circle(0,0,1), green(line(0,0,cos(50*pi/180),sin(50*pi/180)),
 line(0,0,cos(50*pi/180),-sin(50*pi/180))),locate(.16,.18,"50°"),
locate(.67,.4,9cm),locate(.2,.5,r),line(0,0,cos(50*pi/180),0),
red(line(cos(50*pi/180),sin(50*pi/180),cos(50*pi/180),-sin(50*pi/180)))


  )}}}

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.

{{{sin("50°")}}}{{{""=""}}}{{{opposite/(hypotenuse)}}}

{{{sin("50°")}}}{{{""=""}}}{{{9/r}}}

Multiply both sides by r:

{{{red(r)*sin("50°")}}}{{{""=""}}}{{{red(r)*expr(9/r)}}}

{{{r*sin("50°")}}}{{{""=""}}}{{{9}}}

Divide both sides by sin(50°)

{{{r}}}{{{""=""}}}{{{9/sin("50°")}}}

{{{r}}}{{{""=""}}}{{{11.7486656}}}cm. 

Edwin</pre>