Question 776923
One way to handle this is lay the circle onto a cartesian system, centered at the origin, radius of the circle 12 cm.  Examine the two chords separately.


{{{x^2+y^2=12^2}}}
{{{y^2=12^2-x^2}}}
{{{highlight(y=sqrt(12^2-x^2))}}}


The two lengths for x to examine for y are HALF of 5 cm, and HALF of 6 cm.  Evaluate for each, separately, and then SUM the two results for y.  This result is the distance between the two chords.


{{{ drawing( 300, 300, 
          -15, 15,
          -15, 15,
          circle( 0, 0, 12 ),
          circle(0,0,0.2),
          line(-2.5,11.4,2.5,11.4),
          locate( 0, 0, O ),
          blue(locate(2.5,0,2.5)),
          blue(circle(2.5,0,0.2)),
          green(line(-11.9,0,11.9,0))
 )}}}
This picture shows x=2.5, corresponding to a chord length of 5 cm.  The equation for the circle is shown in the symbolic description already described.  The value for y is the distance of the chord from the diameter.  The diameter here is shown as the horizontal axis from -12 to +12.  The distance is computed as {{{y=sqrt(144-2.5^2)}}}.
'
A similar picture and process is done for the 6 cm. chord.