Question 1
How many tangents can a circle have?
- A circle consists of infinitely many points on its boundary.
- Exactly one tangent can be drawn at each point on a circle.
- Therefore, a circle has infinitely many tangents.
Step 1 · Points on a circle and tangents
A circle consists of an infinite number of points on its boundary. Since exactly one tangent can be drawn at each point, a circle can have an infinite number of tangents.
A circle can have an infinite number of tangents.
- External Point Confusion: Conflating tangents on the circle (infinitely many) with tangents from a single external point (which is at most two).
More questions in Exercise 10.1
How many tangents can a circle have?
Fill in the blanks:
(i) A tangent to a circle intersects it in ____________ point(s).
(ii) A line intersecting a circle in two points is called a ____________.
(iii) A circle can have ____________ parallel tangents at the most.
(iv) The common point of a tangent to a circle and the circle is called ____________.
A tangent at a point of a circle of radius meets a line through the centre at a point so that . Length is :
(A) (B) (C) (D) .
Draw a circle and two lines parallel to a given line such that one is a tangent and the other, a secant to the circle.