A Circle Drawing Puzzle
Can you find the center?
Here is a simple puzzle to test your intuition about drawing and geometry
You are given a circle on a piece of paper, a drafting triangle, and a pencil. Can you find the center of the circle?
The solution is below. Take your time to solve this one! Try doing this yourself on a piece of paper. If you peek early, you hurt no one but yourself. Once you look, the problem is gone forever.
Pick any point on the circle, then draw two lines out from it that form a right triangle. Connect the other two points made from the right triangle.
Next, pick another point and repeat the process. It does not matter which point you pick, or how you orient the sides. It is only important that it forms a right angle.
The intersection of these two diagonals, F, will be the center of the circle!
If you want to know why, the basic idea is that you are forming one part of a rectangle in each step. The line connecting the two outer points is the diagonal of the rectangle. The middle of this line will always be equidistant from all corners of the rectangle, meaning it is equivalent to the center of the circle. You have to do this twice to find where the middle is.
This problem was inspired by a similar puzzle from the book Moscow Puzzles. It’s a fantastic source of puzzles like this one.
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