Question 754364
<pre>
{{{drawing(200,200,-50,50,-50,50,
circle(0,0,50),line(0,0,50*.6,-50*.8),
line(0,0,-50*.6,-50*.8), line(50*.6,-50*.8,-50*.6,-50*.8),
locate(-3,9,O), locate(-35,-40,A), locate(32,-40,B),
locate(-3,-40,60),locate(-26,-15,50), locate(17,-15,50)


    )}}}

Draw OC the perpendicular bisector of the chord, which
divides the 60 cm chord into two 30 cm line segments,
AC and BC.  We are looking for the length of OC:


{{{drawing(200,200,-50,50,-50,50,
circle(0,0,50),line(0,0,50*.6,-50*.8),
line(0,0,-50*.6,-50*.8), line(50*.6,-50*.8,-50*.6,-50*.8),
line(0,0,0,-50*.8),locate(-3,9,O), locate(-35,-40,A), locate(32,-40,B),
locate(-3,-40,C),locate(-26,-15,50), locate(17,-15,50),
locate(-15,-40,30), locate(8,-40,30)


    )}}}

Use the Pythagorean theorem on right triangle ACO

OAē = ACē + OCē
50ē = 30ē + OCē
2500 = 900 + OCē
1600 = OCē
&#8730;<span style="text-decoration: overline">1600</span> = OC
40 = OC

Answer: 40 cm.

Edwin</pre>