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Q2(i):
Fill in the blanks : (i) A tangent to a circle intersects it in __________ point (s).
Solution :
Given: A circle and a line segment defined as a tangent to that circle.
To Find: The number of points at which a tangent intersects the circle.
Step 1: Defining a Tangent
By definition, a tangent to a circle is a line that touches the circle at exactly one point. This point is known as the "point of contact" or "point of tangency."
Step 2: Analyzing the Intersection
Let the circle be denoted by $C$ with center $O$ and radius $r$. Let the line be $L$.
If the line $L$ were to intersect the circle at two distinct points, it would be classified as a secant line.
If the line $L$ were to not intersect the circle at all, it would be a non-intersecting line.
Since the line is defined as a tangent, it must satisfy the condition of having exactly one common point with the circumference of the circle.
Step 3: Conclusion
Based on the geometric definition of a tangent in Euclidean geometry, the number of points of intersection is exactly one.
Final Answer: A tangent to a circle intersects it in one point(s).
More Questions from Class 10 Mathematics Circles EXERCISE 10.1
- Q1: How many tangents can a circle have?
- 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.
- 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
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Kazipet, Warangal
2 yrs of
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Ayodhya Nagar, Vijayawada
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Mahipalpur, Delhi
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As an experienced teacher for nine years, I have been teaching to make students interested in the subjects of Maths. My attitude is to help children improve in studies in the best possible way.
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Nerul Sector 20, Thane
10 yrs of
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