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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.

O P Tangent

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).



CBSE Solutions for Class 10 Mathematics Circles


Chapters in CBSE - Class 10 Mathematics


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I started my teaching career in 2005 in that year itself I got a chance to take class in 10 for one month for leave vacancy. After that I got the chance in 2011 in another school, then it continued. Taking class in 10 it was a challenge because responsibilities are more. Both parents and students are in stress, at the same time the school management also. If the results are not satisfactory it will affect to the reputation of the school. So the teachers are alert always .All the students have to face the board. So the preparation of each and every child is important. For that conducting special classes ,morning classes. Conducting evaluations in proper interval. After every evaluation a session with parents in school is very important. Because they are more stressed than students. The year tenth is important because it is the turning point of each student . The effort of all the pupils will be fruitful when we get the good result. Teachers especially those who are taking in class 10 they are not bothered about the salary which the management as paying to them, of course it is a pain to their personal life. Once if we are standing in front of the students our main attention was that whether the concept will be reaching to the pupil in the right meaning and sense. In that time we are not bothered about the payment. If the student got the concept and scored good in exam that was the great reward for teacher. After the schooling that student and parents never forget that teacher in their life every important movements they expect that teachers presence there.

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Bhavana W. Class 10 Tuition trainer in Bhopal
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