All About Circles

Why are circles important?

The circle is one of the most basic shapes in our universe, no matter who you are or where you're from, you've seen a circle. Whether it's the sun in the sky, a clock on the wall, or the wheel on a car, we don't go a day in our life without seeing this shape. So what exactly makes this shape special and how do we define a circle?

What "is" a circle?

It may seem like an obvious question, but we use a very specific definition to determine whether or not something is a circle:

"A circle is every point on a flat surface that is a specific distance from a chosen centre point."

This means that:

  • if it's not flat,

  • if it has straight edges,

  • or if some points are further from the centre than others,

it's not a circle.

links for circles

Glossary

  • Area: the space enclosed by the circle.

  • Arc: a curved line that is part of the circumference of the circle.

  • Centre: the point within a circle that is the same distance from every point of that circle's circumference.

  • Chord: a straight line that joins one point on the circle to another.

  • Circle: the shape containing every point on a flat surface that is a specific distance from a chosen centre point.

  • Circumference: the perimeter of the circle.

  • Compass: a V-shaped device used to draw circles.

  • Compound shape: a shape that is made up of two or more basic shapes.

  • Diameter: the longest straight line distance from one end of the circle to the other.

  • Equidistant: equally distant, or the same distance from.

  • Irrational number: a number that cannot be written as a fraction, whose decimals don't repeat and don't end

  • Plane: a 2-dimensional surface that extends infinitely far.

  • Pi: the ratio for any circle's circumference divided by its diameter. It's about 3.14.

  • Radius: the straight line distance from the centre of a circle to any point on it.

  • Ratio: a comparison of two or more numbers that indicates their values in relation to each other.

  • Secant: a straight line that intersects a circle at two points. (Like a chord, but a secant keeps going).

  • Sector: the part of a circle enclosed by two radii and an arc.

  • Segment: the part of a circle enclosed by a chord/secant and an arc.

  • Semicircle: a shape equivalent to half of a circle, made by "cutting" a circle along its diameter.

  • Tangent: a straight line perpendicular to the radius that only touches one point of the circle.

Key Ideas

As we learn about circles key ideas will be added to this section. It is highly recommended that you have them or some for of them in your notes.

  • The radius is the straight line distance radius is the centre of the circle to any point on the outside.

  • The radius is half the diameter: r =0.5d .

  • The diameter is the straight line distance from one point on the circle, through the centre, to a point on the opposite side of the circle.

  • The diameter is twice the radius: d=2r .

  • A chord is a straight line from one point on the circle to any other point on the circle. Every diameter is a chord, but not every chord is the diameter.

  • A secant is a straight line that passes through 2 points on the circle. It's like a chord that keeps going outside of the circle but it's not actually a chord.

  • A tangent is a straight line is a line that touches (intersects) a circle at just one point and makes a right angle with the radius at that point.

  • Using a ruler to measure the width of our compass allows us to draw a circle with a radius of that length.

  • Pi is the ratio of any circle's circumference to its diameter.

  • Pi is an irrational number. This means it can't be written as a fraction, it does not end, and it does not repeat.

  • We can use pi to calculate the circumference of a circle if we know the diameter or radius. C = πd or C = 2πr.

  • The area of a circle can be calculated using the formula A=πr2 . If we're given circumference of diameter, we can convert them to radius and then find the area.

  • A sector is a "wedge" of a circle's area. It's made by two radii and an arc.

  • A segment is part of a circle's area created by a chord. It's made by a chord and an arc.

  • An arc is a piece of the circle's circumference.

  • We can treat sectors as fractions of the circle's area. For example, if a sector is 1/4 of the circle, the area of the sector will be 1/4 of the area of the circle (sector = 1/4 x A).