SOLUTION: A chord of a circle is 18cm long and subtends an angle of 100 degree at the center. find the radius of the circle.

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