Question:
In a circle of diameter 30 cm, the length of a chord is 15 cm. Find the length of the minor arc of the chord.
Solution:
Diameter = 30 cm
Length of chord $=15 \mathrm{~cm}$
Radius $=15 \mathrm{~cm}[\mathrm{r}=0.5 \times$ diameter $]$
Since the radius is equal to the length of the chord
Hence the formed triangle in the circle is an equilateral triangle.
$\theta=60^{\circ}$
We know that $\mathrm{I}=\mathrm{r} \times \theta$
$I=15 \times 60 \times \frac{\pi}{180}=5 \times \pi=5 \times 3.14=15.7$
Therefore, the length of the minor arc is $15.7 \mathrm{~cm}$