Ruler and Compass Construction 22
Line Parallel to Another Line at a Given Distance

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1. Arbitrary point C on the line
2. Circle centered at C, radius AB
3. Circle centered at D, arbitrary radius
4. Circle centered at E, same radius'
5. Ray CF
6. Circle centered at C, radius AB
7. Circle centered at D, radius AB
8. Circle centered at G, radius AB
9. Parallel line HG

Why it works:
The construction uses a perpendicular to line LM to create a point G at the given distance from LM.
Then point H completes a square, which has parallel sides.