Chapter 10 · Question 1

Define a tangent and a secant of a circle. How many tangents can a circle have?

Answer Revealed

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 touches the circle at exactly one point. This common point is called the point of contact. The word 'tangent' comes from the Latin word 'tangere' meaning to touch. A secant is a line that intersects the circle at two distinct points. A secant can be thought of as the general case, and a tangent is a special case of a secant when the two points of intersection coincide. A circle can have infinitely many tangents because at every point on the circumference of a circle, one and only one tangent can be drawn. Additionally, at most two tangents can be drawn parallel to a given secant.

Key Points

Tangent: intersects circle at exactly one point (point of contact)
Secant: intersects circle at exactly two points
Tangent is the limiting case of a secant where the two points of intersection coincide
Infinitely many tangents can be drawn to a circle (one at each point)

Define a tangent and a secant of a circle. How many tangents can a circle have?