Classify by intersection, not appearance
The number of common points between a line and circle determines whether the line is non-intersecting, tangent or secant. Diagram appearance alone is not the definition.
Learning goals
- Classify a line by its number of common points with a circle.
- Identify tangent, secant and point of contact in diagrams.
- Determine the number of tangents possible from points inside, on and outside a circle.
Concept lesson
Circle parts
A chord joins two points on the circle; a diameter is a chord through the centre; a radius joins centre to circle. These are segments, while tangent and secant classifications concern lines.
Zero, one or two common points
A non-intersecting line has zero common points, a tangent exactly one and a secant two. The unique common point of a tangent and circle is the point of contact.
Tangents from different point positions
No tangent passes through a point inside the circle; exactly one tangent exists at a point on the circle; exactly two tangents can be drawn from a point outside it.
Separate line, chord and contact labels
For a line meeting the circle at P and Q, the full line is a secant and segment PQ is a chord. For a line meeting only at T, the line is tangent and T the contact point.
Count common points
Classify lines in rotated and near-touching diagrams only after marking every common point with the circle.
Line or inside segment?
For each two-point intersection, label the secant line and its chord segment separately; identify radius and diameter distractors.
Move the source point
Move a point from inside to on to outside the circle and predict 0,1,2 tangents, explaining why the count changes at the boundary.
Parallel support lines around a wheel
For a family of parallel lines moved across a circular wheel, classify their intersection states and explain why at most two tangents can be parallel to a given secant direction.
One-mark vocabulary precision
Base the answer on common-point count, name the contact point exactly and distinguish the location of the source point before stating the number of tangents.
Tangent and secant vocabulary mastery
Classify a mixed set of lines, distinguish chord from secant, identify contact points and explain tangent counts for inside, boundary and outside source points.