A curved metal strip is an arc of a circle. Its two ends are 24 cm apart in a straight line, and at its middle the arc stands 8 cm above that straight line. Find the radius of the circle, in cm.

Drop the radius from the centre to the midpoint of the 24 cm chord; it is perpendicular to the chord and cuts it into halves of 12 cm. If the radius is $r$, the centre lies $r-8$ below the top of the arc's rise, so $(r-8{)}^2+12^2=r^2$. Expanding, $r^2-16r+64+144=r^2$, so $16r=208$ and $r=13$ cm. (12 cm is half the chord, not the radius; 26 cm is the diameter; 9 cm comes from the shortcut piece $c^2/(8h)=576/64$ alone, forgetting to add $h/2=4.$)