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Q2(iv):
Fill in the blanks : (iv) The common point of a tangent to a circle and the circle is called __________.
Solution :
Given: A circle and a tangent line that intersects the circle at exactly one point.
To Find: The specific mathematical term used to describe the common point where the tangent line meets the circle.
Step 1: Understanding the Geometry of a Tangent
By definition, a tangent to a circle is a line that intersects the circle at exactly one point. This point is unique because it is the only location on the circumference of the circle that lies on the tangent line.
Step 2: Defining the Terminology
In Euclidean geometry, when a line touches a curve (in this case, a circle) at a single point, that point is referred to as the "point of contact" or the "point of tangency."
Step 3: Logical Deduction
Since the question asks for the name of the common point between the tangent and the circle, we apply the standard geometric definition:
- Let the circle be denoted by $C$.
- Let the tangent line be denoted by $L$.
- The intersection $C \cap L = \{P\}$.
- The point $P$ is defined as the point of contact.
Final Answer: The common point of a tangent to a circle and the circle is called the point of contact (or point of tangency).
More Questions from Class 10 Mathematics Circles EXERCISE 10.1
- Q1: How many tangents can a circle have?
- Q2(i): Fill in the blanks : (i) A tangent to a circle intersects it in __________ point (s).
- Q2(ii): Fill in the blanks : (ii) A line intersecting a circle in two points is called a __________.
- Q2(iii): Fill in the blanks : (iii) A circle can have __________ parallel tangents at the most.
- Q3: 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 :
- Q4: 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.
CBSE Solutions for Class 10 Mathematics Circles
Chapters in CBSE - Class 10 Mathematics
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