Geometry
Tangent
A line that touches the circle at exactly one point — perpendicular to the radius there.
A tangent is a line that just *grazes* a circle — it touches at exactly one point and never cuts inside. At that touch point it makes a perfect right angle with the radius.
Stretch the radius
radius
3.5
3.5
diameter
7.0
7.0
circumference
21.99
21.99
area
38.48
38.48
The two tangent rules
- Tangent ⟂ radius — at the point of contact, the tangent and the radius are perpendicular (90°). The little square in the picture above marks it.
- Two tangents from one point are equal — stand outside a circle, draw both tangent lines to it, and the two touch-point distances are the same length.
- A line is tangent exactly when its distance from the centre equals the radius. Closer → it cuts the circle (a *secant*); farther → it misses entirely.
Your turn
A tangent touches a circle of radius 5. A point P on the tangent is 12 from the centre. How far is P from the touch point?
Watch out
A tangent touches at one point only. A line through two points of a circle is a *chord* (inside) or a *secant* (the full line). 'Touches once' is the whole idea of tangent.