Question

Find the radius of this circle?

Answer 1

The radius of the circle `=r=5` units

Explanation:

Let length of the `archat(AB) =l and C` be the center of this circle.

So , the above image with this points is:

We know that ,

`color(blue)("The arc length of the circle is :"`

`color(blue)(l=r*theta=>r=l/theta`

Where, `l=`arc length ,`r=`radius of circle .

`andcolor(red)( theta="central angle in radians."`

Given that, `l=(10pi)/3 and theta=(2pi)/3`

`:.radius :r=l/theta=((10pi)/3)/((2pi)/3)`
`:.r=(cancel(10pi)^5)/cancel3 xxcancel3/(cancel(2pi))=5`
Hence , the radius of the circle `=r=5` units

Note:

If the central angle is in degrees then,

`color(blue)("The arc length of the circle is :"`

`color(blue)(l=2pir(theta/360)`

Where, `l=`arc length ,`r=`radius of circle .

`andcolor(red)( theta="central angle in degrees."`