Defining a Circle and Right Angles

Background

We can define a line with two points. We can define a circle with one...

Question

Define a circle. Identify some parts of a circle.

Answer

A circle is defined as a figure defined by a single line (the circumference) such that any line segment from the centre of the circle to the circumference is equal to any other such line segment. See below for more terms.

Analysis

We can start with a point:



We can now draw a line around this point such that any line segment we draw from the centre point to the surrounding line is equal:



The purple line is the circle. It is also known as the circumference.

The blue point is the centre of the circle.

The red and black lines are called radii (radii is plural, radius is singular).

If we have a line that runs through the centre of the circle, that is known as a diameter (the black and red lines below):


Notice that the red line and the black line are perpendicular. This means that the circumference is divided into four even pieces. Where we have this situation, the angles between the red and black lines are equal - and are called right angles. We mark right angles with a small square mark:




Note that with the lines being perpendicular, with that one angle being shown as a right angle, they all are (it's understood that all of them are right angles and so all of them need not be marked).

Let's now talk about finding a point along the circumference. 

One way we can measure is by using something called degrees. If we say there are 360 degrees around the circle, then a right angle is 90 degrees (it's one fourth of the way around the circle).

Vocabulary used:

For more information check out these links (comment to add your favourite link):

Where might you have come from?

Fact-orials Index

Geometry:

• Points, Line Segment, Line
• Intersecting, Parallel, Perpendicular Lines

Where might we go?

Numbers:

• Pi

Graphing:

• X, Y Axes 

Geometry:

• Perimeter and Area