Puzzle #31: Circle drawn only on the black squares of a chessboard
Consider a standard chess board. What is the
diameter of the largest circle that can be drawn on the board
whilst only drawing on the black squares.
This is not especially hard, you
just need to visualise it...
Before reading the answer can I interest you in a clue?
The circle could fit entirely with in one
black square, it could be like the green circle below, but we want the
biggest, and that is the red circle:-
There is some logic as to
why this is the largest circle that can be drawn. It has to do with the
fact that a circle can only intercept a straight line at two points,
you can visualise a square around our red circle travelling through the
corners in the same place. (you could calculate the dimensions of this
Using the yellow triangle we
can easily calculate the radius and therefore the diameter of the
circle. We need the hypotenuse of a triangle with opposite and adjacent
sides of 1.5 and 0.5
1.5^2 + 0.5^2
Sqrt(10) / 2
Sqrt(10) = 3.1623
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