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The diagonal of the square is the diameter of the circle (think about it!) so the sides of the square can be pythagorassed ie the square of the diagonal is twice the square of a side.
As an example, consider a circle of diameter 50 units. the square of this is 2500 so every side of the square is the square root of 1250 units which equals sqrt 625 x sqrt 2 or 25 root 2 ie 35.355339 units, or 70.71% of the diameter of the circle.
More basically, the diagonal is the hypotenuse of a 45/45/90 triangle so the sides are in the ratio 1/1/root2 or if you want the hypotenuse to be 1, the sides would be (root 2)/2.
Either way, the sides are root2 times the radius of the circle, which is of course half the diameter. This is in full agreement with the 25 root2 calculated above for a 50 unit diameter circle.
What else can I help you with?
If you have a square inscribed in a circle what is the diameter of the circle congruent to?
The sides of the Square.
What percent of the perimeter of a square is the circumference of the circle?
The answer depends on the relationship between the square and the circle. For example, is the circle inscribed in the square or the square in the circle or something else?
How do you find the radius of an inscribed circle of a square given the area of the square?
Half the square root of the square radius equals the circle radius.
A square is inscribed in a circle of radius 7cm what is the area of the square?
98 cm^2
What is a circle in a square called?
An inscribed circle has its circumference tangent to each side of the square or other type of polygon surrounding it.
Find the dimensions of the rectangle of largest area that can be inscribed in a circle of radius a?
The largest rectangle would be a square. If the circle has radius a, the diameter is 2a. This diameter would also be the diameter of a square of side length b. Using the Pythagorean theorem, b2 + b2 = (2a)2. 2b2 = 4a2 b2 = 2a2 b = √(2a2) or a√2 = the length of the sides of the square The area of a square of side length b is therefore (√(2a2))2 = 2a2 which is the largest area for a rectangle inscribed in a circle of radius a.
If you have a square inscribed in a circle what is the diameter of the circle congruent to?
The sides of the Square.
Can a circle be inscribed in a square?
Yes.
Can a square always be inscribed in a circle?
yes
If you have a circle inscribed in a square what is the diameter congruent to?
The diameter of the circle equals the length of a side of the square
If you are given a square with a circle inscribed in it and the area of the square is 100 m what is the area of the circle?
78.53
What percent of the perimeter of a square is the circumference of the circle?
The answer depends on the relationship between the square and the circle. For example, is the circle inscribed in the square or the square in the circle or something else?
What is the largest square that could fit in a 10-inch diameter circle?
The largest square that could fit in a circle of diameter 10 inches has dimensions 5sqrt(2) inches by 5sqrt(2) inches.
A circle inscribed in a square its diameter is congruent to?
Its diameter is congruent to a side of square.
How do you find the radius of an inscribed circle of a square given the area of the square?
Half the square root of the square radius equals the circle radius.
A circle is inscribed in a square with a side length of 4 If a point in the square is chosen at random what is the probability that the point is in the square but not in the circle?
21.5%
What is a cynosure of Pi?
A circle with a diameter of 2 is the guiding cynosure when Pi is the square of all possible circles: If the square root of Pi defines the side of a square and that square can be inscribed within a circle or enclose a circle, then the diameters of all possible circles between the largest and smallest include the circle of which Pi is its perfect square (a diameter of 2).
