In a circle with center O and radius 5 cm. AB and CD are two parallel chords of lengths 6 cm and x cm, respectively and the chords are on the opposite side of center of the center O. The distance between the chords is 7 cm.
What is the value of x?
Show answer & explanation
Correct answer: C
Explanation
The correct answer is option 3 i.e. 8
Given :
Radius = 5 cm
AB and CD are two parallel chords
Distance between the chords is 7 cm
AB = 6 cm
CD = x cm
Formula used :
Radius2 = (chord/2)2 + (Length between the chord and centre)2 ---- (1)
Calculations :
Let OM = z
ON = 7 - z
Using equation (1) in
⇒ 25 = 9 + z2
⇒ 16 = z2
⇒ z = 4 cm
ON = 7 - z
ON = 3 cm
Using equation (1) in
⇒ 25 = 9 + (x/2)2
⇒ 16 = x2/4
⇒ 64 = x2
⇒ x = 8 cm