The problem is to identify the central angle, a major arc, and a minor arc in a circle with center $r$, diameter $GI$, and $m\angle GFH = 100^\circ$. The first two questions are already answered with correct answers.

1. Problem Description

The problem is to identify the central angle, a major arc, and a minor arc in a circle with center $r$, diameter $GI$, and $m\angle GFH = 100^\circ$. The first two questions are already answered with correct answers.

2. Solution Steps

(a) The given central angle is $\angle GFH$. This answer is already correct, which can be confirmed by visual inspection of the image.

(b) A major arc is an arc that is greater than half the circle. The prompt asks for a major arc. Since $GI$ is a diameter, the arc $GIH$ goes from $G$ to $H$ to $I$. Since the measure of arc $GH$ is $100^\circ$, the arc $GIH$ covers $180^\circ + 100^\circ = 280^\circ$, which is greater than $180^\circ$. So, $GIH$ is a major arc. This answer is already correct in the prompt.

(c) A minor arc is an arc that is less than half the circle (less than $180^\circ$). From the image, we can see that arc $GH$ is a minor arc. Also, arc $IH$ is a minor arc.

Since $GI$ is a diameter, $m\angle GFI = 180^\circ$.

Given that $m\angle GFH = 100^\circ$, then $m\angle HFI = 180^\circ - 100^\circ = 80^\circ$.

Therefore, the measure of arc $HI$ is $80^\circ$. Since this measure is less than $180^\circ$, then $HI$ is a minor arc.

3. Final Answer

HI