Solution:
Given:
In a circle, a radius perpendicular to a chord bisects the chord.
[tex]\begin{gathered} Angle\text{ is bisected;} \\ \theta=\frac{55}{2}=27.5^0 \\ chord\text{ is bisected;} \\ l=\frac{23.5}{2}=11.75in \end{gathered}[/tex]
Hence, the right triangle can be extracted below.
To get the radius of the circle, we use the trigonometric identity of sine.
Hence,
[tex]\begin{gathered} sin\theta=\frac{opposite}{hypotenuse} \\ where: \\ \theta=27.5^0 \\ opposite=11.75 \\ hypotenuse=r \\ \\ sin27.5=\frac{11.75}{r} \\ Cross\text{ multiplying;} \\ r=\frac{11.75}{sin27.5} \\ r=25.45in \end{gathered}[/tex]
Therefore, the radius of the circle is 25.45 in
