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What would be the area of the largest polygon that can be inscribe in a circle whose area is 100 pi?
You can get as close to 100*pi as you like. As you increase the number of sides, the limiting value of the area of the polygon is 100*pi.
How can you find the area of a circle geometrically?
You can do an upper and lower bound by inscribing and circumscribing polygons. The more sides the polygon has, the more precise your answer will be. You inscribe a polygon by having the corners touch the circle's interior, and you circumscribe a polygon by having the midpoint of the sides touch the circle's exterior. Note that the polygon must by equilateral and equiangular for this method to be reasonably simple. Then simply find the area of the inscribed polygon - you know the circle is bigger than it, because the circle contains the polygon and has more space as well. Thus that number is your lower bound. Then find the area of the circumscribed polygon- same logic for the polygon being bigger than the circle. Area of circumscribed is your upper bound. Then typically average your upper and lower bound to get a reasonable estimate of the area of the circle. Of course, solving the problem algebraically is both simpler and more precise, but since you wanted a geometric answer, you got one.
How can a circle be a polygon?
A circle can be a polygon. Sometimes a circle can be a polygon that has infinite number of sides.
What polygon is a circle?
A polygon is a plane area bounded by straight lines. A circle consists of a curved line, not a straight line. Therefore a circle is not a polygon and conversely, no polygon can be a circle.
What is meant by a circle being circumscribed about a polygon?
It means drawing a circle around a polygon in such that each vertex of the polygon is on the circumference of the circle.
The sides of the polygon are chords of the circle?
Then you would draw the polygon inside of the circle, or in other words, "inscribe" the polygon.
A polygon whose vertices are on the circle and whose edges are within the is an?
An inscribed polygon
What would be the area of the largest polygon that can be inscribe in a circle whose area is 100 pi?
You can get as close to 100*pi as you like. As you increase the number of sides, the limiting value of the area of the polygon is 100*pi.
A 3 by 4 rectangle is inscribe in a circle What is the circumference of the circle?
5*pi
Is an circle a polygon?
No, a circle is not a polygon
What is the polygon of a circle?
A circle is not a polygon.
In order to inscribe a circle in a triangle the circle must be placed at the in center of a triangle?
That is correct
How can you find the area of a circle geometrically?
You can do an upper and lower bound by inscribing and circumscribing polygons. The more sides the polygon has, the more precise your answer will be. You inscribe a polygon by having the corners touch the circle's interior, and you circumscribe a polygon by having the midpoint of the sides touch the circle's exterior. Note that the polygon must by equilateral and equiangular for this method to be reasonably simple. Then simply find the area of the inscribed polygon - you know the circle is bigger than it, because the circle contains the polygon and has more space as well. Thus that number is your lower bound. Then find the area of the circumscribed polygon- same logic for the polygon being bigger than the circle. Area of circumscribed is your upper bound. Then typically average your upper and lower bound to get a reasonable estimate of the area of the circle. Of course, solving the problem algebraically is both simpler and more precise, but since you wanted a geometric answer, you got one.
How can a circle be a polygon?
A circle can be a polygon. Sometimes a circle can be a polygon that has infinite number of sides.
A circle inside a polygon where each side of the polygon is tangent to the circle?
the circle is inscribed in the polygon
In order to inscribe a circle in a triangle the circle's center must be placed at the circumcenter of the triangle?
False
In order to inscribe a circle in a triangle the circle's center must be placed at the incenter of the triangle?
That is correct
