The problem asks us to identify which of the given arcs represents a semicircle based on the provided diagram of a circle. A semicircle is an arc that measures 180 degrees, meaning the endpoints of the arc are diametrically opposite, i.e., they form a diameter.

1. Problem Description

The problem asks us to identify which of the given arcs represents a semicircle based on the provided diagram of a circle. A semicircle is an arc that measures 180 degrees, meaning the endpoints of the arc are diametrically opposite, i.e., they form a diameter.

2. Solution Steps

Let's analyze each option:

* Arc BCE: We are given that angle $BHC = 76^{\circ}$. Since $BHC$ is a central angle, the measure of arc $BC$ is also $76^{\circ}$. A semicircle has a measure of $180^{\circ}$. So we need to determine if arc $CE$ has a measure of $180^{\circ} - 76^{\circ} = 104^{\circ}$. We don't have enough information to determine if the arc is actually 104 degrees. However, since $A$ appears to be the top of the circle, $AC$ could represent something close to a diameter. $B$ and $E$ would not be opposite.

* Arc CEA: The straight line passing through point $A$ is a tangent. Therefore, $A$ is the top most point. Also $AC$ looks like it might be a diameter. If $AC$ is a diameter, the arc $CA$ would be equal to 180 degrees. Since $CEA$ looks like a reasonable diameter, let us assume $AC$ passes through point $H$. Then $CEA$ is a reasonable choice.

* Arc GBC: We know arc $BC$ measures $76^{\circ}$. We don't have enough information to determine if the remaining arc $GB$ would give a sum of 180 degrees. But just by inspection, $GB$ is much less than 180-76 =

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* Arc FCB: We know arc $BC$ measures $76^{\circ}$. We don't have enough information to determine if the remaining arc $FB$ would give a sum of 180 degrees. But just by inspection, $FC$ is much greater than

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Based on the diagram, it appears that $AC$ is a diameter, therefore $CEA$ is an approximate semicircle.

3. Final Answer

CEA