Circles
From DT Online
Description
Circles are very familiar but have associated with them terminology, properties and characteristics with which all involved with design and technology should understand.
A particular property of a circle is that its radius can be stepped off around its circumference exactly 6 times. In effect, this constructs 6 equilateral triangles, the interior angles of which are all 60^{0}, and the sum of all angles at the centre of any polygon must equal 360^{0}.
The sides of these equilateral triangles become chords of the circle and should not be confused with the length of an arc, which is longer. Lengths of arcs can be found by dividing the circumference by the number of sides. The circumference is calculated as 2πr or πD (π is a constant obtained by dividing circumference by diameter  i.e. approximately 3.142)".
Constructions
Angle in a SemiCircle 
Note: If angles are drawn in each half of the circle the result would be a particular case of cyclic quadlitaleral which makes it easier to see the more general case that the sum of opposite internal angles of any cyclic quadlitaleral is always equal to 180^{0}. 

Bisecting Chords 


Intersecting Chords Theorem 
Note: This is a particular case of the Intersecting Chords Theorem which states that the relationship (A x B = C x D) is true for any two intersecting chords, whether or not one of them is a diameter


Tangent from a Point Outside a Circle 
Note: This concept is the basis of the design of Centre Squares ( or Centre Finders) 