In a circle of radius 10 cm, two parallel chords of lengths 12 cm and 16 cm are drawn .Find the distance between the chords ,if both the chords are on the opposite sides of the centre.
Answers
Answer:
Let AB and CD be two chords of a circle such that AB is parallel to CD and they are on the opposite sides of the center.
AB=30cm and CD=16cm [ Given ]
Draw OL⊥AB and OM⊥CD.
Join OA and OC.
OA=OC=17cm [ Radius of a circle ]
The perpendicular from the center of a circle to a chord bisects the chord.
∴ AL=
2
AB
=
2
30
=15cm
Now, in right angled △OLA,
∴ (OA)
2
=(AL)
2
+(LO)
2
[ By Pythagoras theorem ]
⇒ (LO)
2
=(OA)
2
−(AL)
2
⇒ (LO)
2
=(17)
2
−(15)
2
⇒ (LO)
2
=289−225
⇒ (LO)
2
=64
⇒LO=8
Similarly,
In right angled △CMO,
⇒ (OC)
2
=(CM)
2
+(MO)
2
⇒ (MO)
2
=(OC)
2
−(CM)
2
⇒ (MO)
2
=(17)
2
−(8)
2
⇒ (MO)
2
=289−64
⇒ (MO)
2
=225
∴ MO=15cm
Hence, distance between the chords =(LO+MO)=(8+15)cm=23cm
solution
Answered By
toppr
How satisfied are you with the answer?
This will help us to improve better
answr
Get Instant Solutions, 24x7
No Signup required
DOWNLOAD APP
girl