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Question
What is the angle subtended at the centre of a circle of radius 6 cm by an arc of length 3 π cm?
Solution
We have
`r=6cm`
length of the arc=`3pi cm`
We will find the angle subtended at the centre of a circle.
Length of the arc=`θ/360xx2pi r`
Substituting the values we get,
3pi=`θ/360xx2pixx6 ` ............(1)
Now we will simplify the equation (1) as below,
` 3pi=θ/360xx2pixx6`..........(1)
`3pi=θ/30xxpi`
`3=θ/30`
`⇒ θ=90°`
Therefore, angle subtended at the centre of the circle is `90°`
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