Chapter 10 · Question 1
Define a tangent and a secant of a circle. How many tangents can a circle have?
Answer
Direct Answer
A tangent to a circle is a line that intersects the circle at exactly one point (called the point of contact). A secant is a line that intersects the circle at two distinct points. A circle has infinitely many tangents — exactly one tangent can be drawn at each point on the circumference.
Simple Explanation
A tangent touches the circle at exactly one point (it just 'kisses' the circle). A secant cuts through the circle at two points. Since you can draw a tangent at every point on the circle's edge, there are infinitely many possible tangents.
Exam-Ready Structure
A tangent to a circle is a straight line that intersects the circle at exactly one point. This point is called the point of contact. A secant is a line that intersects the circle at two distinct points. A tangent may be viewed as the limiting position of a secant, but it is defined separately by its single point of intersection. A circle can have infinitely many tangents because at every point on its circumference, exactly one tangent can be drawn.
Key Points
- Tangent: intersects circle at exactly one point (point of contact)
- Secant: intersects circle at exactly two points
- A tangent is the limiting position of a secant, but is defined by exactly one point of intersection
- Infinitely many tangents can be drawn to a circle (one at each point)