INMO 2023 Problem 6
Euclid has a tool called cyclos which allows him to do the following:
- Given three non-collinear marked points, draw the circle passing through them.
- Given two marked points, draw the circle with them as endpoints of a diameter.
- Mark any intersection points of two drawn circles or mark a new point on a drawn circle.
Show that given two marked points, Euclid can draw a circle centered at one of them and passing through the other, using only the cyclos.
Dataset text NuminaMath olympiads. Quoted with source.
Solutions
No solution is on olymmath yet. Official and human solutions come first when they arrive. AI solutions come after them, with a label.