Question 861182
Half of the longer chord measures {{{14cm/2=7cm}}}.
Half of the shorter chord measures {{{10cm/25cm}}}.
Drawing, not to scale:
{{{drawing(250,300,-3,27,-18,18,
red(circle(0,0,25)),red(circle(0,0,0.3)),
blue(triangle(0,0,20,15,20,0)),
blue(triangle(0,0,24,0,24,-7)),
blue(rectangle(24,0,23,-1)),
blue(rectangle(20,0,19,1)),
green(line(20,15,20,-15)),
green(line(24,7,24,-7)),
locate(11,-3.5,blue(24)),locate(10,7.5,blue(24)),
green(arrow(11,2,20,2)),green(arrow(9,2,0,2)),
locate(9.5,3,x),locate(11.5,-6,y),
green(arrow(13,-7,24,-7)),green(arrow(11,-7,0,-7)),
locate(20.2,8,7),locate(23,-3,5)
)}}} The perpendicular bisector of a chord goes through the center of the circle.
Along with one half of the chord and the radius to one of the chord's ends, it forms a right triangle.
With the two chords, we have two right triangles.
In each of those triangles the hypotenuse measures 24 cm.
The legs of one of those triangles measure {{{x}}}cm and {{{7}}} cm,
so {{{x^2+7^2=24^2}}} --> {{{x^2+49=576}}} --> {{{x^2=576-49}}} --> {{{x^2=527}}} --> {{{x=sqrt(527)=about22.96}}}
The legs of the other triangle measure {{{y}}}cm and {{{5}}} cm,
so {{{x^2+5^2=24^2}}} --> {{{x^2+25=576}}} --> {{{x^2=576-25}}} --> {{{x^2=551}}} --> {{{x=sqrt(551)=about23.47}}}
The distance between the chords is
{{{sqrt(551)-sqrt(527)}}}= approx.{{{23.47cm-22.96cm}}}= approx.{{{0.51cm}}}