Two Arcs, One Line
A compass drawing crosses itself twice, and a straightedge joins the crossings. Open the compass wide and open it narrow — the line it produces never moves. That one fact is bisecting a segment, bisecting an angle and dropping a perpendicular, wearing three different setups.
AM = MB = 105
Both arcs are opened to 140. The line through where they cross meets AB at its midpoint, at a right angle.
- A to B
- 175
- Compass opened to
- 140
Which construction?
Drag B to change the segment.
Ready to try some? Perpendicular bisector worksheets
Where it usually goes wrong
A construction is remembered as a fixed recipe — open the compass to THIS much — so a child who opens it a little wider or narrower than the diagram assumes the answer has changed. The opening is never part of the answer. Any width wide enough for the two arcs to cross puts the crossing on the exact same line, which is the fact a printed diagram, drawn at one width, cannot show.
Try this
- Drag the Compass opening slider from one end to the other. The two circles swell and shrink completely, and the green line through their crossings never moves.
- Switch to Bisect an angle and drag the upper arm wide open, then almost shut. The ray still lands exactly halfway between the two arms every time.
- Switch to Drop a perpendicular and drag P down until it touches the line. The same two arcs still produce a line through P at a right angle, with nothing special done for that case.
Where this goes next
Every compass-and-straightedge construction on this site — copying a segment, copying an angle, inscribing a polygon — builds on this one crossing. Seeing that the width is a free choice is what makes the printed steps read as a proof rather than as instructions to copy exactly.
More about angles and shapes
- Does It Close?an angle steps a circle into a regular polygon exactly when it divides 360° a whole number of times
- Ratios That Never Movesin, cos and tan are ratios rather than lengths, so rescaling a right triangle without changing its angle leaves all three exactly the same
- The Angle That Won't Movean inscribed angle stays exactly half the central angle over the same arc, however far around the circle its vertex moves