1. Problem statement: In the figure, \overline{AD} and \overline{CE} are diameters of circle $P$. The central angle $\angle CPB$ measures $38^\circ$. The central angle $\angle DPE$ measures $93^\circ$. Find the measure of the minor arc $\widehat{AB}$. 2. Formula and important rules: A central angle has measure equal to the measure of its intercepted arc. Therefore $m(\widehat{CB})=m(\angle CPB)=38^\circ$. When two points are endpoints of a diameter they are opposite on the circle, so their direction angles differ by $180^\circ$. 3. Intermediate work and reasoning: Because $A$ and $D$ are opposite and $C$ and $E$ are opposite, the central angle between $A$ and $C$ equals the central angle between $D$ and $E$. Hence $$m(\widehat{AC})=m(\angle DPE)=93^\circ$$. Arc $AC$ is composed of arcs $AB$ and $BC$. So $$m(\widehat{AC})=m(\widehat{AB})+m(\widehat{BC})$$. 4. Solve for the desired arc: Rearrange to get $$m(\widehat{AB})=m(\widehat{AC})-m(\widehat{CB})$$. Substitute the known values. $$m(\widehat{AB})=93^\circ-38^\circ$$ Simplify. $$m(\widehat{AB})=55^\circ$$ 5. Final answer: The measure of minor arc $\widehat{AB}$ is $55^\circ$.