Question

Diameter EG is drawn on circle H and point F is located on the circle such that GF = 8.5inches. If the radius of the circle is equal to 10 inches, then what is the measure of GF to the nearest degree?

Answer 1

`\widehat{GF}=49` degrees

Explanation:

In the figure attached, EG is the diameter of the circle and a point F is located on the circle.

Measure of
`\widehat{GF}` = 8.5 inches

Radius HF = 10 inches

Formula to get the length of arc =
`(\theta)/(360)* (2\pi r)`

8.5 =
`(\theta)/(360)(2\pi)(10)`

θ =
`(360* 8.5)/(20\pi )`

= 48.7°

≈ 49°

Since central angle = measure of the intercepted arc

Therefore,
`\widehat{GF}=49` degrees will be the measure of the given arc GF.