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How do you determine the leg length of a dodecagon circumscribed within a circle with a known radius?
Wiki User
∙ 16y ago
If you mean "inscribed within", the formula is r/(√2 + √6). To see why this is true, consider a "slice" of the dodecagon - a triangle with corners at two connected corners of the dodecagon and at the center of the circle. Its sides are r, r, and s (the length of a side); the angles are 75, 75, and 30. By the Law of Sines, we have that s = r*sin(30)/sin(75). sin(75)=sin(30+45)=sin(30)cos(45)+cos(30)sin(45). We know the values for sine and cosine of 30 and 45; when we substitute them into the sin(30)/sin(75), we get 1/(√2 + √6). This gives us the formula above.
Wiki User
∙ 16y ago
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The side of a square is 20 cmfind the areas of the circumscribed and inscribed circles?
The radius length r of the inscribed circle equals to one half of the length side of the square, 10 cm. The area A of the inscribed circle: A = pir2 = 102pi ≈ 314 cm2 The radius length r of the circumscribed circle equals to one half of the length diagonal of the square. Since the diagonals of the square are congruent and perpendicular to each other, and bisect the angles of the square, we have sin 45⁰ = length of one half of the diagonal/length of the square side sin 45⁰ = r/20 cm r = (20 cm)(sin 45⁰) The area A of the circumscribed circle: A = pir2 = [(20 cm)(sin 45⁰)]2pi ≈ 628 cm2.
How do you find the area of a hexagon that is inscribed in a circle?
The area of any hexagon is 6(0.5)(L)(L sin 60o) = 3L2 sin 60o, where L is the length of one side and is also the radius of the circumscribed circle.
How can the radian measure of an angle determine the arc length on the unit circle?
The radian measure IS the arc length of the unit circle, by definition - that is how the radian is defined in the first place.
How would you construct a right triangle given the length of a leg and the radius of the circumscribed circle?
To construct a right triangle given the radius of the circumscribed circle and the length of a leg, begin with two ideas. First, the diameter of the circle is equal to twice the radius. That's pretty easy. Second, the diameter of the circle is the length of the hypotenuse. The latter is a key to construction. Draw your circle, and draw in a diameter, which is the hypotenuse of the right triangle, as was stated. Now set you compass for the length of the leg of the triangle. With this set, place the point of the compass on one end of the diameter (the hypotenuse of your triangle), and draw an arc through the circumference of the circle. The point on the curve of the circle where the arc intersects it will be a vertex of your right triangle. All that remains is to add the two legs or sides of the triangle. Draw in line segments from each end of the hypotenuse (that diameter) to the point where your arc intersected the curve of the circle. You've constructed your right triangle. Note that any pair of lines that is drawn from the ends of the diameter of a circle to a point on the curve of the circle will create a right triangle.
What is the length of a circle known as?
The length around a circle is the circumference The length across a circle is the diameter
The side of a square is 20 cmfind the areas of the circumscribed and inscribed circles?
The radius length r of the inscribed circle equals to one half of the length side of the square, 10 cm. The area A of the inscribed circle: A = pir2 = 102pi ≈ 314 cm2 The radius length r of the circumscribed circle equals to one half of the length diagonal of the square. Since the diagonals of the square are congruent and perpendicular to each other, and bisect the angles of the square, we have sin 45⁰ = length of one half of the diagonal/length of the square side sin 45⁰ = r/20 cm r = (20 cm)(sin 45⁰) The area A of the circumscribed circle: A = pir2 = [(20 cm)(sin 45⁰)]2pi ≈ 628 cm2.
How do you determine length and width of a circle?
there is no length or width of a circle. There is radius and circumference and the line that goes all the way through the center to the other side of the circle, which is twice the radius. But there is no length or width of a circle.
How do you determine the length of the radius on a circle?
The radius of a circle is defined as the distance from the centre-point to the circumference.
How do you find the area of a hexagon that is inscribed in a circle?
The area of any hexagon is 6(0.5)(L)(L sin 60o) = 3L2 sin 60o, where L is the length of one side and is also the radius of the circumscribed circle.
What is the formula for calculating perimeter of dodecagon?
Assuming the shape is a regular dodecagon, the formula for calculating the perimeter for a dodecagon of side length n is equal to 12n.
How can the radian measure of an angle determine the arc length on the unit circle?
The radian measure IS the arc length of the unit circle, by definition - that is how the radian is defined in the first place.
How do you determine the length of a circle?
The length of the radius of a circle is measured by a straight line from the centre to the edge. The length of the diameter of a circle is measured by a straight line from one side, through the centre, to the other side. The length of the circumference is calculated by multiplying the diameter by the constant pi... which is usually approximated to 3.1416.
How do you find the radius given the chord length?
If you are given a chord length of a circle, unless you are given more information about the chord, you can not determine what the radius of the circle will be. This is because the chord length in a circle can vary from a length of (essentially) 0, up to a length of double the radius (the diameter). The best you can say about the radius if given the chord length, is that the length of the radius is at least as long has half half the chord length.
How would you construct a right triangle given the length of a leg and the radius of the circumscribed circle?
To construct a right triangle given the radius of the circumscribed circle and the length of a leg, begin with two ideas. First, the diameter of the circle is equal to twice the radius. That's pretty easy. Second, the diameter of the circle is the length of the hypotenuse. The latter is a key to construction. Draw your circle, and draw in a diameter, which is the hypotenuse of the right triangle, as was stated. Now set you compass for the length of the leg of the triangle. With this set, place the point of the compass on one end of the diameter (the hypotenuse of your triangle), and draw an arc through the circumference of the circle. The point on the curve of the circle where the arc intersects it will be a vertex of your right triangle. All that remains is to add the two legs or sides of the triangle. Draw in line segments from each end of the hypotenuse (that diameter) to the point where your arc intersected the curve of the circle. You've constructed your right triangle. Note that any pair of lines that is drawn from the ends of the diameter of a circle to a point on the curve of the circle will create a right triangle.
What is the length of a circle known as?
The length around a circle is the circumference The length across a circle is the diameter
What is the measure of each arc of a circle that is circumscribed about a regular pentagon?
Angular measure: 2*pi/5 radians or 72 degrees. or Length of arc: 2*r*pi/5 units or 144*r units, where r is the radius.
What is a pie in mathematics?
pi in mathematics is used to determine the circumference of a circle. if you take a piece of string the length of the diameter of the cicle it would go around the circle 3.14159265358978 times (pi).
