We need the perpendicular to ( OA ) at ( O ), but without a midpoint/perpendicular bisector tool (would be extra move unless done cleverly). But in Euclidea, you can construct a perpendicular through a point on a line by:
Euclidea is a geometry puzzle game that transforms the ancient rigor of Euclidean constructions into a minimalist digital logic game. While the game begins with simple tasks like constructing midpoints or perpendicular bisectors, it quickly escalates into challenges that require profound lateral thinking. One of the most iconic early hurdles is found in Level 2.8, titled "Square." The standard solution requires five moves (5E), but the true test of mastery lies in the elusive 3-star solution, which requires completing the construction in a mere three moves (3E). euclidea 2.8 3e
Circle ( \omega ) with center ( O ) and point ( A ) on ( \omega ). Goal: Construct all vertices of a square inscribed in ( \omega ) using exactly 3 elementary moves. We need the perpendicular to ( OA )
Let’s define: Circle center ( O ), given point ( A ) on the circle. One of the most iconic early hurdles is found in Level 2
This third circle, drawn through the centers of the first two circles, completes a system of arcs that perfectly locates the remaining vertices of the square. Because Euclidea’s game logic recognizes the construction of the final shape based on the intersection points, the square is "solved" the moment the geometry aligns, without the player needing to manually draw the four sides. This highlights a core philosophy of the game: a shape exists once its defining constraints are established, not just when its outline is inked.
