Question

12"retest: CirclesOASelect the correct answerArc XY located on circle A has a length of 40 centimeters. The radius of the circle is 10 centimeters. What is the measure of the correspondingcentral angle for XY in radians?O B.OC.OD. 34TResetSubmit TestNextReader Tools

Answer 1

step 1

Find out the circumference

`C=2\pi r`

where

r=10 cm

substitute

`\begin{gathered} C=2\pi(10) \\ C=20\pi\text{ cm} \end{gathered}`

Remember that

The circumference subtends a central angle of 2pi radians

so

Applying proportion

Find out the central angle by an arc length of 40 cm

`\begin{gathered} (2\pi)/(20\pi)=(x)/(40) \\ \\ x=4\text{ rad} \end{gathered}`

therefore

The answer is 4 radians Option B