The problem is to identify a major arc in the given circle. A major arc is an arc of a circle having a measure greater than or equal to 180 degrees but less than 360 degrees. We are given that $F$ is the center of the circle and $GI$ is a diameter. Also, the measure of $\angle GFH$ is $100^\circ$.

1. Problem Description

The problem is to identify a major arc in the given circle. A major arc is an arc of a circle having a measure greater than or equal to 180 degrees but less than 360 degrees. We are given that $F$ is the center of the circle and $GI$ is a diameter. Also, the measure of $\angle GFH$ is $100^\circ$.

2. Solution Steps

A diameter divides the circle into two semicircles, each measuring $180^\circ$. Since $GI$ is a diameter, the arc $GI$ is a semicircle. We also know the measure of $\angle GFH$ is $100^\circ$, so the measure of arc $GH$ is $100^\circ$.

We are looking for a major arc. A major arc is an arc with a measure greater than $180^\circ$.

Consider the arc $GIH$. The measure of arc $GI$ is $180^\circ$, and the measure of arc $GH$ is $100^\circ$. So the measure of arc $GIH$ is the measure of arc $GI$ + measure of arc $GH$ = $180^\circ + 100^\circ = 280^\circ$. Since $280^\circ > 180^\circ$, the arc $GIH$ is a major arc.

Consider the arc $HIG$. The measure of the complete circle is $360^\circ$. We know arc $GH$ is $100^\circ$, so arc $HIG$ = $360^\circ - 100^\circ = 260^\circ$. Since $260^\circ > 180^\circ$, the arc $HIG$ is a major arc.

3. Final Answer

HIG