1.

AB and CD are two parallel chords of a circle which are on opposite sides of the centre such that AB=10 cm, CD=24 cm and the distance between AB and CD is 17 cm.Find the radius of the circle.

Answer» Let `r` is the radius of the circle and `O` is the center of fthe circle.
We can draw a diagram with the given details.
Please refer to video for the diagram.
From the diagram,
In `Delta OAN`,
`r^2 = 5^2+(17-x)^2->(1)`
In `Delta OMC`,
`r^2 = 12^2+x^2->(2)`
From (1) and (2),` 5^2+(17-x)^2 = 12^2+x^2`
`=> 25+289+x^2-34x = 144+x^2`
`=>34x = 170=> x = 5`
Putting value of `x` in (2),
` r^2 = 12^2+5^2 = 169`
`r = 13` cm
So, radius of the circle is `13` cm.


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