If I had a checkersboard with black and white squares, each 5 by 5 cm. What's the radius of the. . .?

Question

If I had a checkersboard with black and white squares, each measuring 5 by 5 cm. What's the radius of the largest square which can be drawn on the board with the circle only touching the white? Rounding is needed to the nearest hundreth of the centimetre.
This is the only question I need help with figuring out on my homework.
Thanks. <3. It would be much appreciated If you helped me with this question.

Someone please help me! It's due tomorow! =(

But can't you draw a circle diagonally?

I think they mean that you can draw it diagonally.

Answer 1

I guess it was an oversight, but in your problem you said, "What's the radius of the largest square which can be drawn on the board with the circle only touching the white?" Are we working with a square or a circle here? Since the rest of it talks about circles, I guess we'll have to work with that.

The other question is what it means by "only touching the white." That is, can the circle cross an intersection of squares, so that it doesn't enter a black square but does touch a corner of a black square? The answer to this will determine the answer to the question.

If we cannot touch a corner or an edge of a black square, then the best we can do is to draw a circle within one of the white squares. There is no such thing as a "diagonal circle" (do you mean an oval or an ellipse?), and any other circle would have to cross through a black square. Since each square is 5 cm on each side, the radius of a circle centered in a square would be 2.5 cm. However, remember that we cannot even touch the edge of a black square, so reduce this to 2.49 cm. This will give you the largest circle which does not extend to the edge of the black squares surrounding the white square in which the circle is drawn.

If we CAN touch an edge or corner, there is a larger circle that can be drawn. It will be a circle drawn around a black square--passing through all of the white squares that surround the black square. Since it cannot cross through a black square, it must touch all of the corners (what would be described as a circle circumscribing the square). So the center of the circle is at the center of a black square, and the radius is half the length of the diagonal of the black square. That radius measures 2.5 times the square root of 2, or about 3.54 cm.

The only thing I don't know for certain is whether the circle is allowed to touch the edge of a black square or not.

Answer 2

This is the best that i can be of any help...

Based on the question, there is only one possible way to draw a circle without having any black contacts..

Bear in mind that you cannot simply draw a circle within a white box as that will indicate the four tangents of the circle will be touching the black border...

In order to accomplish an all white contact..

-Pick any 1 white square.. Determine the centre of that square.. You can do so by drawing diagonals to find the intersection.. That point of intersection will be the centre point of the circle you are about to draw...

-Next, you have to know that in order for the circle to not have any contact with the black, it has to pass through the four corners of the white square...

-Now, you have to determine the radius. The radius of the circle will be from the centre of the square to the corner of the white square (since the circumference does passes through the corners)..

-You can even calculate the radius.. The radius of the circle is equivalent to half the length of the square diagonal... *Hope you are still with me...* Use Phytagoras Theorem to calculate the diagonal... [diagonal = sqrt(5^2 + 5^2) = 7.0710678118654755]...

-Divide this answer by two and you will get the radius of the circle... which is... 3.53553390593273775... rounded off to the neares hundredth... 3.54cm....

All the best.. Oh ya.. Do keep me updated if possible as to whether the answer is right or not...


Cheers.. (",)

Answer 3

Sounds like a trick question. If it can only be touching the white, that means no black. And that means the circle is confined to a single square. And if each square is 5cm by 5cm, that means the circle has to fit within that. So the circle can have a maximum diameter of 5cm. Half that is the radius. So the radius would be 2.5cm.