Geometry · Foundation · 9 min
Compass & straightedge
A perpendicular bisector can be constructed using only equal compass radii and a straightedge.
WHAT HAPPENS IF…Why must the compass radius exceed half AB?
Loading the mathematical model…
Choose a compass radius greater than half AB. The two equal-radius circles meet above and below AB. Both intersection points are equidistant from A and B; their joining line is the perpendicular bisector. Subtracting the two distance-squared equations also gives x=0 in the symmetric coordinates shown.
A detail that matters
The compass opening must stay the same for both circles.
Keep the connection going
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