Two parallel chords are drawn in a circle of diameter 10 m. The length of one chord is 8m and the distance between the two chords is 6 m. Find the length of the other chord.
Show answer & explanation
Correct answer: D
Explanation
The correct answer is option 4 i.e. 8 m
According to question,
AB and PQ are two chords and O is the center of the circle.
M is the mid-point of AB and N is the mid-point of PQ.
OB = OQ = 5 m (Radius of a circle)
AB = 8 m and MN = 6 m
Let OM be x, then
MB = 8 ÷ 2 = 4 m
⇒ In right-angled triangle MOB, (OB)2 = (OM)2 + (MB)2
⇒ 52 = OM2 + 42
⇒ OM 2 = 25 – 16 = 9
⇒ IF = 3 m
⇒ Putting the value of x, ON = 6 – 3 = 3 m
⇒ In right-angled triangle ONQ, (OQ)2 = (ON)2+ (NQ)2
⇒ 52 = 32 + NQ2
⇒ NQ2 = 25 – 9 = 16
⇒ NQ = 1–√6= 416 =4 m
⇒ PQ = 2NQ
⇒ PQ = 2 × 4 = 8 m