Math 6H ( Periods 3, 6, & 7)

Circle 4-5

A circle is the set of all points in a plane at a given distance from a given point O ( called the center)
A segment joining the center to a point on the circle is called a radius (plural: radii) of the circle ALL radii of a given circle have the same length and this length is called the radius of the circle
A segment joining two points on the circle is called a chord. However a chord passing through the center is called a diameter of the circle. The ends of the diameter divide the circle into two semicircles. The length of the diameter is called the diameter of the circle.

The perimeter of a circle is called the circumference

The quotient
circumference ÷ diameter
is the same for all circles regardless of their size. This quotient is denoted by the Greek letter ∏ ( pronounced 'pie') No decimal gives ∏ exactly.-- but a good approximation is 3.14

If we denote the circumference by C and the diameter by d
we have
C ÷ d = ∏.
We can manipulate this formula to several useful forms:

C = ∏d
or d = C ÷ ∏ .
In addition since we know that d = 2r we can also have the following:

C = 2 ∏ r
or r = C ÷(2∏)

When using the approximate 3.14 for ∏ , give your answer in three digits-- as the book explains.
In addition, use the approximately equal to symbol ≈ when you have replaced ∏ .

A polygon is inscribed in a circle if all of its vertices are on the circle. See the diagram on Page 129 for a good example of an inscribed triangle.

It can be shown that three points NOT ON A LINE determine a circle.