InterMath Dictionary
Circle
Parts of a Circle
The circle is the set of points that lie on the blue curve. The points that lie inside this curve are not part of the circle (they form what is called a disk.) A circle is an example of a closed curve because you can begin at one point on the circle, trace it, and end up where you started without crossing or retracing any part of the circle.
If the circle is divided into two unequal parts or arcs, the smaller arc is called the minor arc and the larger arc is called the major arc.
The center of a circle is the same distance from all points on the circle. Point C is the center of this circle. This distance from the center of the circle to any point on the circumference is called the radius (indicated by r in the picture at the right). Any line segment whose endpoints are the center and a point on the circle is also called the radius.
Point E is not the center of this circle. Point E is not even part of the circle.
Based on this definition, "same distance from all points", can a square have a center?
Circles in Your World
Sundials and quilts are often made of circles.
The unusual floor plan of an apartment displays several arcs. Are they major or minor arcs?
Check for Understanding
Identify each of the parts of the circle at the right:
a) segment AC
b) point A
c) the red curve, clockwise from D to C
d) the blue curve, clockwise from C to D
Choose each answer from the menus.
External Links to Extend Basic Understanding
Circles at Math.com: Read more about and practice naming parts of circles.
Related Investigations on InterMath to Challenge Teachers
Four dogs: Explore the paths of four dogs who each start at a different vertex of a square. Angles in a Circle: Investigate how the location of an angle's vertex affects its relationship to the measure(s) of the arc(s) it intercepts. Equation of a Circle: Find the equation of a circle based on its radius, center, and locus of points. Optimizing Triangles using Radii: Find the triangles with maximum and minimum area if two sides of the triangle are determined by radii of the circle. Grazing for Mooey: How many square meters of grazing ground does Mooey the cow have?
Top of Page
Measurements Related to a Circle
The circumference (indicated in red) is like the perimeter around the circle, indicating the length or distance around the circle. (It's similar, but not exactly alike. Perimeter deals with straight lines while circumference deals with curved lines.)
As the number of sides of an inscribed regular polygon increases (see figures below), the perimeter of the regular polygon gets closer to the circumference of the circle. In other words, the perimeter of the regular octagon more closely approximates the circumference of the circle than does the perimeter of the regular pentagon or the equilateral triangle.
The ratio of the circumference of any circle to its diameter is always a number that is close to 3.1416. This number is called pi and is written . Pi is an irrational number, which means it cannot be written as an exact decimal. We usually estimate pi with 3.14, 3.1416, or 22/7.
The line segment that goes through the center of the circle and whose endpoints are on the circumference of the circle is called a diameter. The length of this line segment is also called the diameter.
The line segment that has one endpoint as the center of the circle and the other endpoint on the circumference of the circle is called the radius of the circle. What do you think the relationship is between the radius and the diameter? If you aren't sure, measure the diameter and radius of a circle. What do you notice?
Measurements Related to a Circle in Your World
What part of the bike wheel shown below is a radius? Why might you be interested in knowing about the circumference of the wheel?
Identify the following vocabulary terms based on a description:
a) the distance across a circle, passing through the center
b) the distance around a circle
c) the distance from the circle to its center
Calculate each of the following values in circle A.
a) the radius
b) the diameter
c) the circumference
d) the area
Type the word pi to represent . For example, if your answer was 20, then input 20pi into the text area.
Enter each answer in the left column followed by pressing tab
Circles at Math.com: Practice naming parts of circles.
Mrs. Glosser's Math Goodies--Circumference: Read more about circles and practice calculating circumference.
Circumference computation at aaamath.com: Practice calculating circumference.
Mrs. Glosser's Math Goodies--Circle Area: Read more about circles and practice calculating area.
Tangential Circles: Compare the area and circumference of a circle inscribed in a region between two intersecting circles. Equal Areas: Construct a circle with five equal regions that do not intersect at the circle's center. Tangent Along the Diameter: Find the relationship between the area of a circle and the areas of the tangent circles along the circle's diameter. Changes in the Circumference: Explore how changing the diameter of a circle affects its circumference. Area of a Sector: Determine the relationship between the area of a circle's sector and the radius and central angle of the circle, and between the arc length of a circle and the radius and central angle of the circle.
Examples of Chords
The far right example shows the diameter as a chord of the circle. So the length of a chord is equal to or less than the diameter. Non-Examples of Chords
Circles at Math.com: Read more about chords and practice identifying them.
Intersecting Chords: Determine the relationship between segments formed by the intersection of two chords of a circle. Perpendicular Bisectors: Describe the significance of the perpendicular bisectors of two segments that have endpoints on a given circle. Equidistant Chords: Determine the relationship between two segments that have endpoints on a circle if the segments are the same perpendicular distance away from the center of the circle. Segments on a Secant: Find an equation that relates segments on a secant.
The figures below show circumcircles (in red) of regular polygons.
The polygons do not have to be regular, but they do need to be convex, as the following illustrates.
Inscribed Parallelogram: What must be true about a parallelogram that is inscribed in a circle? N-Sided Circle?: Compare the perimeters of polygons to the circumference of a circle.
These concentric circles have the same center C. As the picture illustrates, the radii do not have to increase at a constant rate. In other words, the area between circles does not have to be the same "width".
Circle R is the center of three concentric circles. If BR=4, AB=3, and YX=1, then find:
a) YZ
b) RX
c) WB
Circles at Math.com: Practice identifying radii in concentric circles.
Target Areas: Determine the area of a target formed by concentric circles. Ready Fire Aim!: If three darts are thrown at a bulls-eye, what are the possible totals? Impossible Scores: What is the highest score below 100 that is impossible to score on a given dart board?
In the figure, the line EF, which contains the diameter of circle A, divides the circle into two semi-circles, arc EGF and arc EHF.
The degree measure of a semi-circle is 180 degrees, half that of a full circle which is 360 degrees.
Circle Inscribed in a Semicircle: Compare attributes of a circle that is inscribed in a semicircle to attributes of that semicircle. Inscribed in a Semi-Circle: Examine the angles inscribed in a semicircle. Half as much may be right: Explore triangles inscribed in semicircles.
| How-To Page |Welcome Page | Main InterMath Page