Question

The length of one of two chords of a circle is 12 cm. If the chords are 6 cm and 7 cm respectively away from the centre of the circle, calculate the length of the second chord...
Please with explanation ​

Answer 1

Answer:

2√23 cm or  9.59 cm to the nearest hundredth

Step-by-step 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.