how can i get largest square in circle

• Feb 14th 2011, 12:56 PM
mido22
how can i get largest square in circle
i want to get maximum area of square can be drawn in a circle if its diamemter is "d"

eg:
7 ---->24.5
12 ---->72
29 ---->420.5
• Feb 14th 2011, 01:32 PM
topsquark
Quote:

Originally Posted by mido22
i want to get maximum area of square can be drawn in a circle if its diamemter is "d"

eg:
7 ---->24.5
12 ---->72
29 ---->420.5

The largest square in the circle would be one that touches the circle on all four vertices, so the diagonal across the square will be the same as the diameter of the circle...

-Dan
• Feb 14th 2011, 01:33 PM
e^(i*pi)
If I understand correctly the diameter will also be the longest diagonal across the square.

From Pythagoras you know that $\displaystyle d^2 = 2a^2 \text{ and } d = a\sqrt{2} \implies a = \dfrac{d}{\sqrt{2}}$ where a is the side length.

(nb: because side length must be greater than 0 I have discarded the negative root)

Now what do you know about the area of a square?
• Feb 15th 2011, 01:28 AM
mido22
Quote:

Originally Posted by e^(i*pi)
If I understand correctly the diameter will also be the longest diagonal across the square.

From Pythagoras you know that $\displaystyle d^2 = 2a^2 \text{ and } d = a\sqrt{2} \implies a = \dfrac{d}{\sqrt{2}}$ where a is the side length.

(nb: because side length must be greater than 0 I have discarded the negative root)

Now what do you know about the area of a square?

thx very much
the area of square will be : r*r*2
• Feb 15th 2011, 05:36 AM
CaptainBlack
Quote:

Originally Posted by mido22
thx very much
the area of square will be : r*r*2

If you think r is the radius of the circle then NO.

Read what the others have posted above. The diagonal of the square will be equal to a diameter of the circle.

So what is the side of a square it its diagonal is d?

CB