`A B\ a n d\ C D` are two parallel chords of a circle such that `A B=10\ c m\ a n d\ C D=24\ c mdot` If the chords are on the opposite sides of the centre and the distance between them is `17\ c m ,\ ` find the radius of the circle.

Explanation

`A B\ a n d\ C D`
are two
parallel chords of a circle such that `A B=10\ c m\ a n d\ C D=24\ c mdot`
If the
chords are on the opposite sides of the centre and the distance between them
is `17\ c m ,\ `
find the radius of the circle.
Given AB and CD are two chords of a circles on opposite sides of the centre.
Draw perpendiculars `OE \and\ OF` onto `AB \and\ CD` respectively from centre `O.`
`AE = EB = 5cm \and\ CF = FD = 12 cm`
Distance between two chords`=17cm`
Distance between `O \and\ F =xcm`
Distance between `O \and\ E=17-xcm`
In `/_\ OEB, OB^2=OE^2+EB^2`(Pythagoras theorem)
`(17-x)^2+5^2`....(1)
In `/_\ OFD ,OD^2=OF^2+FD^2`(Pythagoras theorem)
`=x^2+12^2`.....(2)
But `OB=OD`( radii of the same circle)
from comparing 1 and 2
`(17-x)^2+5^2=x^2+12^2`
`289+x^2-34x+25=x^2+144`
`34x=170`
`x=5`
substitution in equation ii) ,`OD^2=5^2+12^2`
`OD=13`
Radius of the circle is `13 cm.`