Two parallel chords are drawn in a circle of diameter 20 cm. The length of one chord is 16 cm and the distance between the two chords is 12 cm. The length of the other chord is:
Answer & explanation
Correct answer: option 3
In ΔBOM,
According to the pythagoras theorem,
BO2 = BM2 + OM2
= 102 = 82 + OM2
= 100 = 64 + OM2
OM = \(\sqrt {100 - 64}\) = 6
OM = ON = 6
Similarly in ΔCON,
CO2 = CN2 + ON2
= 102 = CN2 + 62
= CN = \(\sqrt {100 - 36}\) = 8
CD = 2 × CN
CD = 2 × 8 = 16