1. **Problem statement:** Construct triangle POR with $PQ=8cm$, $\angle QPR=45^\circ$, and $PR=6cm$. 2. **Step 1: Draw base PQ.** Draw a line segment $PQ=8cm$. 3. **Step 2: Construct angle $\angle QPR=45^\circ$.** At point $P$, construct an angle of $45^\circ$ with line $PQ$. 4. **Step 3: Mark point R on the ray from P at $45^\circ$ such that $PR=6cm$.** Using a compass, set radius to $6cm$ and mark point $R$ on the ray. 5. **Step 4: Draw triangle POR.** Connect points $Q$ and $R$ to form triangle $POR$. 6. **Step 5: Construct perpendicular bisector of $PQ$.** Find midpoint $M$ of $PQ$ (at $4cm$ from $P$). Draw a line perpendicular to $PQ$ at $M$. 7. **Step 6: Name midpoint of $PQ$ as $S=5$.** (Assuming $S$ is midpoint, but $5$ likely a label.) 8. **Step 7: Draw circle with center $S$ passing through $P$.** Using compass centered at $S$ with radius $SP=4cm$, draw the circle. 9. **Step 8: Construct tangent from $P$ to the circle.** Draw tangent line from $P$ touching the circle at point $T$. 10. **Step 9: Find $OT$ and angle $\angle POT$.** Draw line $OT$ from center $O$ to tangent point $T$. Calculate $\angle POT$ using triangle properties. 11. **Step 10: Write theorem used.** The tangent to a circle is perpendicular to the radius at the point of contact. **Final answer:** Triangle $POR$ constructed with given dimensions, perpendicular bisector, circle, tangent $PT$, and angle $\angle POT$ found using tangent-radius perpendicularity.