Suppose you have a board with tan and grey squares, each square measuring 5 cm by 5 cm...?

Question

What's the largest circle that can be drawn on the board such that the entire circumference of the circle is only touching grey?

Answer 1

If it is a checker pattern, the circle would have to extend off the board; so that only two points are tangent to the grey, as close to the end 5th cm as possible. Technically, according to that, the circle can be infinitely big.

Answer 2

Assuming alternately colored squares (each square 5 cm
by 5 cm) then the diameter of the largest circle than can be drawn so the circumference lies within the board and only touches grey will be (5 - x) cm where x is arbitrarily small but non-zero. The size of the board is irrelevant. Note: if touching at a single point, as with a tangent line (or at the corner points of the squares) is allowed then the answer is 5cm exactly. Note: because a circle has a constant curvature, the circumference cannot pass through corner points of the squares even if allowed, without also cutting an arc through at least 2 tan squares, with the exception that the diagonal of one tan square is the diameter of a circle that passes through the the 4 corners of the tan square and the remainder of the circumference passes through only grey squares (4 of them).It's diameter would be sqrt(5^2 +5^2)=5*sqrt(2) cm

Answer 3

Assuming that the tan and grey squares alternate both horizontally and vertically, i.e. they form a "checkerboard patter", then...

If by "only touching grey", you mean that the circle cannot even contact a tan square at a single point, then the circle must have a radius of 5-n centimeters, where n is positive and lim(n) approaches zero. If n were equal to zero, then the circle would touch four different tan squares at four different points.

If instead you also allow the circle to touch tan squares at a point but do not allow the circumference to "enter" a tan square, then the largest possible circle has a radius of 5/sqrt(2) centimeters. This circle would have a tan square inscribed within it, but would touch the tan squares only at single points at the corners.

Answer 4

The largest circle cannot be deteremined as the size of the board is not given and that the arrangements of the coloured tiles are not given as well..

Nevertheless... On the other hand... One can determine the smallest circle...

Assuming that the tiles are arranged alternately in which no two same coloured tiles are placed side by side, the diameter of the smallest circle ever possible will be approx. in the range of 5.1cm to 9.9cm..

Reason being so... The centre of the circle is locatted at the tan tile.. And the grey tiles are located in the north, east, south and west of the tan tile.. Having that fact, the circumference of the circle actually passes through the four corners of the tan tile..

Thus, we meet the requirement in which the entire circumference of the circle is only touching grey...

cheers...(",)

Answer 5

You don't tell us anything about the size of the board or how the squares are laid out on the board. Different arrangements will give different answers.

Answer 6

Not enough information? All I can haphazard is a circle of radius 2.5 cm.

Answer 7

Not enough information. How are the squares laid out?

Without more information I'd say < 5cm

Answer 8

50*pi