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The length of two chords AB and CD ...

The length of two chords AB and CD of a circle with its centre O are equal . If `angle AOB 60^(@)` and `CD = 6cm` then calculate the length of the radius of the circle .

Text Solution

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In `Delta AOB, OA = OB [ because " radii of same circle "]`
`therefore angle OAB = angle OBA `
Now ` angle AOB + angle OAB = 180^(@) `
` or 60^(@) , + angle OAB + angle OAB = 180^(@) [ because angle OBA = angle OAB]`
` or 2 angle OAB = 120^(@) or angle OAB = angle OAB]`
In `Delta OAB , angle OAB = angle OBA = angle AOB = 60^(@)`
`therefore Delta OAB ` is equilateral , `therefore ` OA = OB = AB
But AB = CD = 6 cm `therefore ` OA = OB = 6 cm
`therefoe ` Radius of the circle = 6 cm
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