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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.

O P Tangent

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).



CBSE Solutions for Class 10 Mathematics Circles


Chapters in CBSE - Class 10 Mathematics


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experience 15 yrs of Exp students 5 students
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Mathematics professional trainer with 15 years of teching experience in CBSE school.
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Dedicated and passionate educator with over 10 years of experience teaching Mathematics and Science to students of Classes 8th to 12th across multiple boards — CBSE, ICSE, IGCSE, IB MYP, and IBDP. Founder of Ishaan Tuitions, Pune, specializing in personalized one-to-one coaching and small group sessions designed to strengthen conceptual understanding and academic performance. Expertise also includes preparing students for competitive examinations such as SAT and IIT-JEE Mains, with a strong record of improving analytical thinking and problem-solving abilities.

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Ashish Bhatia Class 10 Tuition trainer in Surat
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experience 15 yrs of Exp students 13 students
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Top Tutor on Urban Pro | Maths & Sci Educator | IB, ICSE, IGCSE, CBSE | 17+ yrs Exp. | 1600 + hrs
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