Question 300074
<pre><font size = "indigo"><b>
We want to find the red arc at the top of this circle
of radius 10.

{{{drawing(200,200,-11,11,-11,11,

 green(line(-6,8,6,8)),locate(0,8,12),

red(arc(0,0,20,-20,53.13010235,126.8698976)),

green(arc(0,0,20,-20,126.8698976,413.1301024)) 

 )}}}

we draw in two 10 cm radii to the ends of the 12 cm chord

{{{drawing(200,200,-11,11,-11,11,
locate(3,4,10), locate(-4,4,10),
 green(line(-6,8,6,8)),locate(0,8,12),
locate(-.3,3,theta), 
red(arc(0,0,20,-20,53.13010235,126.8698976)),

green(arc(0,0,20,-20,126.8698976,413.1301024)) 
green(line(-6,8,0,0)), green(line(6,8,0,0)) 
 )}}}

We need to find angle {{{theta}}}, which subtends
the red arc. We use the law of cosines, with our
calculator in radian mode.  If you haven't had the
law of cosines yet, we can do it by considering
two right triangles.  Post again if you need us to
do it that way.

{{{cos(theta)=(10^2+10^2-12^2)/(2*10*10)=0.28}}}

{{{theta=1.287002218radians}}}

We use the arc length formula:

{{{s=r*theta=10*1.287002218=12.87002218cm}}}

Edwin</pre>