Question

Two parallel chords are drawn in a circle of diameter $30cm$.The length if one chord is $24cm$ and the distance between the two chords is $21cm$ find the length of the other chord.

Answer 1

AD=Diameter=30 cm

CD=Chord=24 cm

$x+y=21$

Again, $y^2+{12}^2={15}^2$

$\Rightarrow y^2={15}^2-{12}^2$

$\Rightarrow y^2=81$

$\Rightarrow y=9$

$x=21-9=12$

Now, ${12}^2+a^2={16}^2$

$a^2={16}^2-{12}^2=81$

$\Rightarrow a=9$

Length of the chord AB$=2\times 9=18cm$