Question

If the chord of a circle is 23.5 in. long and subtends a central angle of 55º, what is the radius of the circle?

Answer 1

Given:

In a circle, a radius perpendicular to a chord bisects the chord.

`\begin{gathered} Angle\text{ is bisected;} \\ \theta=(55)/(2)=27.5^0 \\ chord\text{ is bisected;} \\ l=(23.5)/(2)=11.75in \end{gathered}`

Hence, the right triangle can be extracted below.

To get the radius of the circle, we use the trigonometric identity of sine.

Hence,

`\begin{gathered} sin\theta=(opposite)/(hypotenuse) \\ where: \\ \theta=27.5^0 \\ opposite=11.75 \\ hypotenuse=r \\ \\ sin27.5=(11.75)/(r) \\ Cross\text{ multiplying;} \\ r=(11.75)/(sin27.5) \\ r=25.45in \end{gathered}`

Therefore, the radius of the circle is 25.45 in