LESSON THIRTY-SECOND.
THE CIRCLE AND ITS LINES.
If the straight line c a were a string made fast at c, with a sharp pencil-point at the other end a, and the pencil-point were moved towards d, what line would be drawn?
What kind of a line would it be?
If the pencil-point continued to move in the same direction until it returned to the starting-point a, what curved line would be drawn, naming it by all the points in it which are marked?
The plane figure bounded by this curve is called a “circle.”
What point is at the centre of this figure?
A circle is a plane figure bounded by a curved line, all points of which are equally distant from the centre.
The curved line is called a “circumference.”
The circumference of a circle is the curve which bounds it.
Name a straight line that joins two points in the circumference.
It is called a “chord.”
A chord is a straight line that joins two points of a circumference.
Read six chords in the diagram.
Which two of these chords pass through the centre?
They are called “diameters.”
A diameter is a chord that passes through the centre.
Name a line that joins the centre with a point of the circumference.
It is called a “radius.”—(Plural, radii.)
A radius is a straight line that joins the centre to a point of the circumference.
Read five radii.
Which is farther from the centre, the point a or the point d?
Can the radius c d be greater than the radius c a? Or greater than c v, or c o?
Then all radii of the same circle are equal to each other.
What do we call the lines o d, c d, c o?
What part of the diameter o d is the radius o c?
Name a chord that is produced without the circle.
It is called a “secant.”
A secant is a chord produced.
Name two secants.
If the chord d i were made a secant, would it become longer or shorter?
In how many points does the straight line l m touch the circumference?
It is called a “tangent.”
A tangent is a straight line that touches a circumference in only one point.
Name three tangents.
