Two parallel chords on the same side of the centre of a circle are 12 cm and 20 cm long and the radius of the circle is cm. What is the distance between the chords?
Show answer & explanation
Correct answer: C
Explanation
The correct answer is option 3 i.e. 2 cm.
OQ = OS = 5 √13 cm
PQ = 12 cm, RS = 20 cm, PM = MQ = 12/2 = 6 cm and RN = NS = 20/2 = 10 cm
In Δ MQO
OQ2 = MQ2 + MO2
⇒ (5 √13)2 = 62 + OM2
⇒ OM2 = 325 – 36 = 289
⇒ OM = √289 = 17
In Δ NSO
OS2 = NS2 + NO2
⇒ (5 √13)2 = 102 + NO2
⇒ ON2 = 325 – 100 = 225
ON = √225 = 15
As we know,
OM = MN + ON
⇒ 17 = MN + 15
⇒ MN = 17 – 15 = 2 cm