This line is your perpendicular bisector. You have successfully bisected the segment and created a right angle! Why This Works (The Geometry Behind It)
If the level allows you to start with arbitrary points: euclidea 2.8 solution
The Euclidea level task requires you to construct a line tangent to a circle at a specific point on its circumference. While the standard construction using a perpendicular line is straightforward, the level's 3E (Elementary Moves) challenge is a famous "brain teaser" because it can be solved without ever finding or using the circle's center. 3E Solution Breakdown (The "OO/" Method) To achieve the 3E goal, you use two circles and one line: This line is your perpendicular bisector
(using elementary moves counting circles as 1E): Same as above — two circles then line (3E actually, no). But Euclidea’s E-star counts circle+circle+line=3E, so 3E is minimal for E-star. Wait, they say 2E possible? No, because line is 1E if using elementary move, so total 3E. But the game’s “E” counts circles/lines/perpendiculars as 1 each. So 2E means 2 moves total: impossible here because tangent needs a line. So 2E must be two circles and no line? Not possible. So 2E not possible. Their E-star solution is actually 3E: two circles + one line. But they show 2E for some problems? Likely 2.8 is 3L and 3E stars. While the standard construction using a perpendicular line
Yes! That’s it: