Question

In circle O, radius OQ measures 9 inches and arc PQ measures 6 pie inches. What is the measure, in radians, of central angle POQ? edge

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Answer 1

The circle has circumference
`18\pi\,\mathrm{in}`. If
`m\angle POQ=\theta`, then

`(6\pi\,\rm in)/(18\pi\,\rm in)=\frac\theta{2\pi\,\rm rad}\implies\theta=\frac{2\pi}3\,\mathrm{rad}`

Answer 2

Answer:
`(2\pi)/(3)\text{ radians}`

Explanation:

We know that the formula to calculate the length of arc having central angle 'x' is given by :-

`l=x r`, where r is radius of the circle.

Given : In circle O, radius OQ =
`l=9\text{ inches}`

The measure of arc PQ =
`6\pi\text{ inches.}`

The measure of central angle POQ ( in radians ) is given by :-

`x=(l)/(r)\\\\\Rightarrow\ x=(6\pi)/(9)}\\\\\Rightarrow\ x=(2\pi)/(3)`

Hence, the measure of central angle POQ =
`(2\pi)/(3)\text{ radians}`