1. **Problem statement:** We have a circle with center $O$ and a circumscribed angle $A$ around it. We want to find the length of segment $\overline{AB}$. Given are an angle of $73^{\circ}$ and lengths 4 and 3 (likely sides or segments related to the circle and angle). 2. **Understanding the problem:** Since $A$ is circumscribed about circle $O$, $A$ is a point outside the circle from which tangents $AB$ and $AC$ are drawn to the circle. The angle at $A$ between these tangents is $73^{\circ}$. The lengths 4 and 3 likely represent the distances from $A$ to points $B$ and $C$ on the circle or related segments. 3. **Key property:** The tangents from a point outside a circle are equal in length. So, $AB = AC$. 4. **Using the angle between tangents:** The angle between the two tangents from $A$ is $73^{\circ}$. The distance from $A$ to the center $O$ is the length of the segment $AO$. 5. **Formula for length of tangent:** The length of the tangent from $A$ to the circle is given by $$AB = \sqrt{AO^2 - r^2}$$ where $r$ is the radius of the circle. 6. **Using the given lengths:** If 4 and 3 are the distances from $O$ to $B$ and $C$ or the radius and distance $AO$, we need to clarify. Assuming 4 is $AO$ and 3 is $r$. 7. **Calculate $AB$:** $$AB = \sqrt{4^2 - 3^2} = \sqrt{16 - 9} = \sqrt{7}$$ 8. **Final answer:** The length of $\overline{AB}$ is $\sqrt{7}$ units.