Let, length of AB = 6cm and length of CD = 8cmRadius of circle = 5cmOB = OC = 5cmWe know that a perpendicular drawn from the center of a circle on its chord bisectsthe chord.AM = MB = 3cmAlso, CN = ND = 4cmIn ΔOMB,⇒ OB2 = OM2 + MB2⇒ 52 = OM2 + 32⇒ OM2 = 25-9⇒ OM2 = 16⇒ OM = 4cmIn ΔONC,⇒ OC2 = ON2 + CN2⇒ 52 = ON2 + 42⇒ ON2 = 25-16⇒ ON2 = 9⇒ ON = 3cmDistance between AB and CD = OM + ON = 4 + 3 = 7cmHence the correct option is D.

Q. 1 G4.4( 13 Votes )

Choose correct al

Class 9th MHB - Math Part-II 6. Circles

Answer :

Let, length of AB = 6cm and length of CD = 8cm

Radius of circle = 5cm

OB = OC = 5cm

We know that a perpendicular drawn from the center of a circle on its chord bisects

the chord.

AM = MB = 3cm

Also, CN = ND = 4cm

In ΔOMB,

⇒ OB² = OM² + MB²

⇒ 5² = OM² + 3²

⇒ OM² = 25-9

⇒ OM² = 16

⇒ OM = 4cm

In ΔONC,

⇒ OC² = ON² + CN²

⇒ 5² = ON² + 4²

⇒ ON² = 25-16

⇒ ON² = 9

⇒ ON = 3cm

Distance between AB and CD = OM + ON = 4 + 3 = 7cm

Hence the correct option is D.

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