1. The problem states that the angle $\angle ACB$ is half of the arc $\widehat{AB}$. This is a classic property in circle geometry. 2. The formula used here is the Inscribed Angle Theorem, which states: $$\angle ACB = \frac{1}{2} \times \widehat{AB}$$ where $\angle ACB$ is an inscribed angle and $\widehat{AB}$ is the measure of the intercepted arc. 3. This means the inscribed angle is always half the measure of the arc it intercepts. 4. If you know the measure of the arc $\widehat{AB}$, you can find the angle $\angle ACB$ by dividing the arc measure by 2. 5. Conversely, if you know the inscribed angle $\angle ACB$, you can find the arc measure by multiplying the angle by 2. This property is fundamental in solving many circle geometry problems involving inscribed angles and arcs.