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Question
The lengths of two parallel chords of a circle are 6 cm and 8 cm. if the smaller chord is at a distance of 4 cm from the centre, what is the distance of the other chord from the centre?
Solution
ance of smaller chord AB from center of circle= 4cm OM=4cm
`MB=(AB)/2=6/2=3cm`
`In ΔOMB`
`OM^2+MB^2=0B^2`
`(4)^2+3^2+OB^2`
`16+9=OB^2`
`OB=sqrt25`
`OB=5cm`
In Δ OND
`OD=OB=5cm`
`ND=(CD)/2=8/2=4cm`
`ON^2+ND^2=OD^2`
`ON^2=(4)^2=(5)^2`
`ON^2=25-16=9`
`ON=3`
So, distance of bigger chord from circle is `3cm`
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