Question

In circle H with m \angle GHJ= 90m∠GHJ=90 and GH=20GH=20 units, find the length of arc GJ.

HELP!!

Answer 1

Since $\angle GHJ=90^\circ$, arc $GJ$ is a quarter of the circumference of circle $H$. The formula for the circumference of a circle is $C=2\pi r$, where $r$ is the radius, so the circumference of circle $H$ is:

$$C=2\pi \cdot 20 = 40\pi$$

Since arc $GJ$ is a quarter of the circumference, its length is:

$$\frac{1}{4} \cdot 40\pi = 10\pi$$

Therefore, the length of arc $GJ$ is $10\pi$ units.