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Q2(ii):
Fill in the blanks : (ii) A line intersecting a circle in two points is called a __________.
Solution :
Given: A circle and a line that intersects the circle at two distinct points.
To Find: The specific mathematical term used to describe such a line.
Step 1: Analyzing the definition of a line intersecting a circle
In geometry, the relationship between a line and a circle is categorized based on the number of points of intersection:
1. If a line does not touch the circle at all, it is called a non-intersecting line.
2. If a line touches the circle at exactly one point, it is called a tangent.
3. If a line intersects the circle at two distinct points, it is called a secant.
Step 2: Applying the definition
The problem states that the line intersects the circle in two points. By the standard definition in Euclidean geometry, a line that cuts through a circle at two points is defined as a secant line.
Step 3: Conclusion
Since the line passes through the interior of the circle and intersects the circumference at two distinct points, the term that satisfies the condition is "secant".
Final Answer: A line intersecting a circle in two points is called a secant.
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(iii): Fill in the blanks : (iii) A circle can have __________ parallel tangents at the most.
- Q2(iv): Fill in the blanks : (iv) The common point of a tangent to a circle and the circle is called __________.
- 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
Top Tutors who teach Circles
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