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. LESSON THIRTY-THIRD. REVIEW. Read six chords. (DIAGRAM 24.) Why is _i d_ a chord? What is a chord? Name two diameters. Why is _a j_ a diameter? What is a diameter? Is every chord a diameter? Is every diameter a chord? Name five radii. Why is _c a_ a radius? What is a radius? A diameter is equal to how many radii? Are all radii equal to each other? Are all chords equal to each other? Are all diameters equal to each other? Name two secants. Why is either one a secant? What is a secant? Name three tangents. Why is _a b_ a tangent? What is a tangent? Is a tangent inside of a circle or outside of it? Is a chord inside or outside of a circle? Is a secant within or without a circle?