Q. 1 G4.3( 12 Votes )
Choose correct alternative answer and fill in the blanks.
The lengths of parallel chords which are on opposite sides of the center of a circle are 6 cm and 8 cm. If radius of the circle is 5 cm, then the distance between these chords is .....
A. 2 cm
B. 1 cm
C. 8 cm
D. 7 cm
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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