Question

In a circle of radius 17 cm, two parallel chords are drawn on opposite side of a diameter. This distance between the chords is 23 cm. If the length of one chord is 16 cm then the length of the other is

• A. 34 cm
• B. 15 cm
• C. 23 cm
• D. 30 cm

Answer 1

Answer: (D)

30 cm

Given: Radius of the circle = 17 cm

Distance between the two parallel chords = 23 cm

$AB||CD$ and LM = 23 cm

Join OA and OC.

$\therefore OA=OC=17cm$

Let OL = x cm, then OM = (23 - x) cm

AB = 16 cm

Now in right $\Delta OAL$, $O{A}^2=O{L}^2+A{L}^2$

$\Rightarrow (17{)}^2=x^2+A{L}^2\Rightarrow 289=x^2+A{L}^2$

$\Rightarrow x^2=289-A{L}^2=289-{\left(\frac{16}{2}\right)}^2$

$=289-64=225=(15{)}^2$
$\therefore x=15cm$

and OM = 23 - x = 23 - 15 = 8 cm

Now in right $\Delta OCM$, $O{C}^2=O{M}^2+C{M}^2$

$\Rightarrow (17{)}^2=(8{)}^2+C{M}^2\Rightarrow 289=64+C{M}^2$
$\Rightarrow C{M}^2=289-64=225=(15{)}^2$
$\therefore CM=15cm$

$CD=2\times CM=2\times 15=30cm$