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two parallel chords of a circle of length 12 cm and 16 cm live on the same side of circle if the distance between the chord is 2 cm. find the radius of the circle.
Answers
Answer:
correct answer
Step-by-step explanation:
Correct option is A)
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