Question 1
How many tangents can a circle have?
A circle has many points, and a tangent can be drawn at each point.
Tangent to a circle: A line that touches a circle at exactly one point is called a tangent. That single point is called the point of tangency. Unlike a secant (which cuts through the circle at two points), a tangent just grazes the circle at one point and is perpendicular to the radius at that point.
Step 1 — Points on a circle
Let's consider a circle. A circle is a collection of points. It has an infinite number of points. These points are all on its boundary.
Step 2 — Tangents at points
We can draw a line at each point. This line touches the circle at only one point. This special line is called a tangent. Since there are infinite points. A circle can have infinite tangents.
Answer
A circle can have an infinite number of tangents.
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 PQ at a point P of a circle of radius 5 cm meets a line through the centre O at a point Q so that OQ = 12 cm. Length PQ is :
(A) 12 cm (B) 13 cm (C) 8.5 cm (D) cm.
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.