Question

Line segments AB and CD are diameters of the circle shown below. If this circle has a circumference of 10 inches, what is the length of arc BC in inches?

Answer 1

SOLUTION

Now let us re-draw the sector

Now, I have taken the center of the circle as O. Since the two diameters intersect at the centre, the lines CO and BO are also radius of the circle.

Now let us find the radius of the circle

$\begin{gathered} \text{circumference of a circle = 2}\pi r \\ \text{circumference has b}e\text{en given as 10 inches } \\ 10\text{ =2}\pi r \\ 10\text{ = 2}\times3.14\times r \\ 10=6.28r \\ r=\frac{10}{6.28} \\ \\ r=1.59\text{ inches } \end{gathered}$

So, since we have found r, let us find the length of arc BC

$\begin{gathered} \text{length of arc = }\frac{\theta}{360}\times\text{circumference of circle } \\ \\ \text{length of arc = }\frac{144}{360}\times2\pi r \\ \\ \text{length of arc = }\frac{144}{360}\times10 \\ \\ \text{length of arc = 4 inches } \end{gathered}$