Download Circle Geometry - Indigenous Perspectives in Mathematics

Circle Geometry
Grade 9
Lesson 8.1: Properties of Tangents to a Circle
(adapted from Math Makes Sense 9)
Objectives: Students will discover the relationship between a tangent and a radius, and
then solve related problems
Materials Required:
Compass
Straight Edge
Protractor
The circle is a central and significant symbol in many First Nations’ Cultures. The
pictures shown here are from our Grade 9 Culture Camp. They show some of the
Tipis that we slept in.
The tipi has a circular base and is shaped like a cone. This shape helps to make
the structure strong because the wind swirls around the structure rather than
blows against it.
Traditionally, the tipi was held down by rocks. This created a ring of rocks all
around the circumference of the bottom of the tipi. These rocks were left behind
when the tipi was moved. You can still find old stone tipi rings on the prairie in
Canada. I visited a sacred site last Spring near Three Hills where we found
several tipi rings. They can be hard to find, so you have to look closely and
carefully. Next time you are on the prairie, have a look around. You just might find
an old tipi ring.
If we were to draw the base of a tipi or the tipi ring, we could do the following steps:
1. Get out a piece of paper and your geometry set
2. Construct a large circle in the center of the page
At Culture Camp, we had trouble with one of the donkeys that lived out there. He
wanted to visit the inside of our tipi – even when we did not invited him! One
solution to this was to create a barrier in front of the tipi. We wanted the barrier to
run at the front of the tipi where the door was. In order to draw this on our paper
we could:
3.
4.
5.
6.
7.
Draw a radius
Draw a line that touches the circle only at the endpoint of the radius
Measure the angle between the endpoint and the line.
Repeat with another radius
What do you notice?
This kind of line has a special name. It is called a TANGENT line. A line that
intersects a circle at only ONE point is a TANGENT to the circle (all other lines intersect
circle 0 or 2 times)
The point where the tangent intersects the circle is the Point of Tangency
Determining the Measure of an Angle in a Triangle:
Point 0 is the center of the tipi
AB is tangent to the tipi stone circle
 AOB = 63º
How do you determine the angle at A?
The interior angles of a triangle are ___________________________.
What other angle do you know? Angle at O is ______________________.
What other angle do you know? Angle at B is ________________________.
Therefore the angle at A is: