Question

Circle D is shown. Line segment G D is a radius, D F is a radius, and D E is a radius. Angle G D F is 126 degrees, and angle F D E is 41 degrees. Point C is on the circle within angle G D F and point H is on the circle within angle G D E.
Which statements are correct? Check all that apply.

Arc GF is a major arc.
One major arc is Arc G H E.
Arc FE is a minor arc.
The measure of Arc F E is 41°.
The measure of Arc G C F is equal to the measure of ∠GDE.
Arc GHE is a semicircle.

Answer 1

Correct statements:
- Arc FE is a minor arc.
- The measure of Arc FE is 41°.

Reason: central angle FDE = 41°, so the minor arc FE measures 41°. Angle GDF = 126° so minor arc GF = 126° (not major); ∠GDE = 126°+41° = 167°, so arc GHE (lying inside ∠GDE) measures 167° (not a semicircle), and arc GCF equals 126° which is not equal to ∠GDE.