Answer:
2√23 cm or 9.59 cm to the nearest hundredth
Explanation:
The 12 cm chord is 6 cm away from the centre and the other chord is 7 cm away from the centre.
If we draw 4 radii from the ends of the 2 chords to the centre and 2 lines perpendicular from the centre to the 2 chords we have 2 pairs of congruent right triangles.
So by Pythagoras:
r^2 = 6^2 + 6^2 ( the given chord)
r^2 = 7^2 + x^2 where x is 1/2 * length of the second chord.
Therefore:
7^2 + x^2 = 6^2 + 6^2
x^2 = 36+ 36 - 49 = 23
x = √23
and length second chord = 2√23.