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A circle is a basic shape used in geometry which is representative of a closed curve creating two regions which separate a plane. These two regions are known as the interior and exterior. Additionally, another feature of a circle is that all points are an equal distance from the center.

There are a few measurements which are associated with circles:

  1. Radius: The radius can be taken from any point on a circle and it is equal to the distance from a point on a circle to the center.
  2. Circumference: The circumference is equal to the entire distance around a circle following a circle’s edge.
  3. Diameter: The diameter is a measurement which calculates the distance from one point on a circle directly across to the corresponding point on the other side of a circle. The diameter is twice the value of the radius.

Figure 1. This figure provides an example of a circle. The radius is represented by the black line extending to the center of the circle. The diameter is depicted by the red line which passes through the center of the circle. The circumference is illustrated by the dashed line which acts as the edge of the circle.

Furthermore, the value the concept of pi (∏) is also tightly correlated with the shape of a circle. Pi is always equal to approximately 3.14 and describes the ratio of the circumference to the diameter. Regardless of the size of a circle, this ratio of pi will always be the same.


∏ = circumference/diameter 

Equation of the circle

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Prove: For any given circles R and R' in C_oo, there is a mobius transformation T such that T(r)=R'. Further, we can specify that T take any 3 points on R onto any 3 points of R'. If we do specify Tz_j for j=2,3,4 (distinct z_j in R), then T is unique.

Euclidean circle

Let K be the Euclidean circle with equation...See attached file for full problem description.

Two distinct, nonparallel lines are tangent to a circle....

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Here is the question to prove: Given a circle with radius Q, and a point on the circle R and considering a circle with diameter QR. Let a line go through R and intersect the smaller circle at S and the larger circle at T. Construct a diagram and prove that RS=ST.

Cylinder Inscribed in a Sphere and X-Intercepts of a Parabola

1. When a cylinder is inscribed in a sphere, the sphere's diameter is equal to the diagonal of the cylinder's height and diameter. Relate height of the cylinder to the radius of the sphere. 2. Which of x-values does the parabola defined by y = (x-3)2-4 cross the x-axis?

Revolutions of a tire

Two cars with new tires are driven at an average speed of 60 mph for a test drive of 2000 miles. The diameter of the wheels of one car is 15 inches. The diameter of the wheels of the other car is 16 inches. How many revolutions does each tire make?

Two circles, A and B, touch each other at exactly one point...

Two circles, A and B, touch each other at exactly one point, as shown in the diagram below. The equation of circle A is . Circle B has centre (1, k + 1) and radius 4. Please see the attached file for the fully formatted problems. (Not to scale) a) i) Find the completed square form of x2 - 18x Find the completed sq

Algebra - circles,, center and radius

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A pipe is supported by a block and a wall.Find the pipe radius in terms of the block height and its distance from the wall. A block with height "b" is placed a distance "a" from a wall, to hold in place a pipe with radius "R" (the pipe is supported by the wall on the other side - see attached figure). Find the radius "R" in ter

Finding the Area of a Circle using the Unit Circle

Please see the attached file for the fully formatted problems. Given square is 11*11, unit square is 1*1 without using any algebraic equation by using scissors or folding it, we can find the area of 11*11 square in terms of unit square. With a similar idea we can do triangles (Main triangle and unit triangle).

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