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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.
What else can I help you with?
Find the dimensions of the rectangle of largest area that can be inscribed in a circle of radius a in C programming?
Find the dimensions of the rectangle of largest area that can be inscribed in a circle of radius a in C programming
Find the dimensions of the rectangle of largest area that can be inscribed in a circle of radius 4 inches?
Approximately 5.66x5.66 in. Or root32 x root32
What parallelogram can be inscribed in a circle?
if a parallelogram is inscribed in a circle it is always a rectangle...............
What is the area of the rectangle of largest area that can be inscribed in a circle of radius r?
It is 2*r^2.
Can a rectangle always be inscribed in a circle?
Yes.
If a parallelogram is inscribed in a circle then it must be a?
If a parallelogram is inscribed in a circle then it must be a cyclic quadrilateral.
Is a parallelogram inscribed in a circle always a rectangle?
Yes. The corners must be right angles for it to be inscribed on the circle.
Can a circle be inscribed in a rectangle?
Yes! It can(: you draw the circle in the rectangle with its top and bottom touching the top and bottom sides of the rectangle
If a parallelogram is inscribed in a circle it must be a rectangle?
Yes, a parallelogram inscribed in a circle must be a rectangle. This is because a circle's inscribed angle theorem states that the opposite angles of a cyclic quadrilateral (a quadrilateral inscribed in a circle) must be supplementary. In a parallelogram, opposite angles are equal, which can only hold true if all angles are right angles, thus making the parallelogram a rectangle.
What is the area of the largest circle that will fit into a rectangle with dimensions 8.5 cm by 10.6 cm?
56.7 cm2
A 3 by 4 rectangle is inscribed in circle. What is the circumference of the circle?
the diagonal of the rectangle will be the diameter of the circle which equals 5 so the circumference will be 5pie or 15.70units.
A 5 by 12 is inscribed in a rectangle what is the radius of the circle?
6.5 units
