1. **Problem Statement:** Construct a circle passing through three points $P$, $Q$, and $R$ that are not collinear. 2. **Key Concept:** A unique circle can be drawn through any three non-collinear points. The center of this circle is the intersection of the perpendicular bisectors of any two segments formed by these points. 3. **Step 1:** Construct the line segment $PQ$. 4. **Step 2:** Construct the line segment $PR$. 5. **Step 3:** Construct the perpendicular bisector of segment $PR$. This is done by: - Finding the midpoint $M$ of $PR$. - Drawing a line perpendicular to $PR$ at $M$. 6. **Step 4:** Construct the perpendicular bisector of segment $PQ$ similarly. 7. **Step 5:** The intersection point $O$ of these two perpendicular bisectors is the center of the circle. 8. **Step 6:** Use $O$ as the center and the distance $OP$ (or $OQ$ or $OR$) as the radius to draw the circle passing through $P$, $Q$, and $R$. This method ensures the circle passes exactly through all three points.