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kasperpeulen / euclidthegame

A geometry game based on Euclid's Elements.
euclidthegame.org
MIT License
447 stars 74 forks source link

level 13 Unaccepted answer #272

Closed KiGoAll closed 10 years ago

KiGoAll commented 10 years ago

unaccepted13 A -Center of Big Circle

leftysrevenge commented 10 years ago

There's a more thorough method to guarantee the center of a circle. Your blue points are arbitrary, so they may not be exact. Try using chord properties to help find center.

KiGoAll commented 10 years ago

Point A could be placed anywhere on circle. The main idea is to draw a circle, which radius is twice larger. Point A is center of big circle, point B is Intersection of two circles. Then AB is diameter, and its midpoint should be center of smaller point

leftysrevenge commented 10 years ago

How would you determine that your larger circle's radius equals the diameter of the smaller without using arbitrary points? With your current construct, I don't believe that's possible.

Hexstream commented 10 years ago

@KiGoAll It wouldn't matter even if you could place your arbitrary A and B points in a pixel-perfect manner such that they were "exactly" at opposite ends of the circle and thus would be a diameter passing through the middle pixel of the circle. They're still arbitrary points, so there's no proof that they pass through the exact center of the circle. Your AB segment is just an arbitrary chord of the circle.

Try moving one or both of your arbitrary points around by right-click-dragging it and see if your solution still appears to work visually.

KiGoAll commented 10 years ago

Ok, I see.