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NCERT Solutions for Maths Class 10 Chapter 10 Circles Exercise 10.1 - FREE PDF Download
Class 10 Maths NCERT Solutions for Chapter 10 Circles Exercise 10.1 provides clear answers to all the questions in this exercise. This helps students understand the basics of circles, such as properties and rules about tangents. By studying these solutions, students can clear their doubts and gain a solid understanding of circle geometry.
Exercise 10.1 Class 10 focuses on problems involving tangents to a circle. Understanding and using the rules related to tangents is important for learning this topic. Vedantu's solutions offer step-by-step explanations to help students apply these concepts easily. The CBSE Class 10 Maths Syllabus offers students the fundamental understanding they need to do well in maths examinations.
Glance on NCERT Solutions for Maths Chapter 10 Exercise 10.1 Class 10 | Vedantu
Class 10 Circles Exercise 10.1 solutions discuss circles and tangents, including their properties and definitions.
A circle is defined as the set of all points in a plane that are equal in distance from a fixed point known as the centre.
A tangent to a circle is a straight line that intersects the circle at only one point.
The place where a tangent intersects the circle is known as the point of tangency.
The tangent at any point on a circle is perpendicular to the radius drawn to the point of tangency.
The length of a tangent from an outside point to the circle.
The theorem states that tangent segments extended from an exterior point to a circle are of equal length.
Various problems and solutions use these definitions and attributes to help others understand the concepts.
Ex 10.1 Class 10 solves problems involving tangents from an external point and related theorems.
There are 4 fully solved questions in Chapter 10 Exercise 10.1.
Formulas Used in Class 10 Chapter 10 Exercise 10.1
Diameter of a circle = D = 2 × r (where r is the radius of the given circle)
Circumference of a circle = C = 2 × π × r (where r is the radius of the given circle)
Area of a circle = A = π × r2 (where r is the radius of the given circle)
NCERT Solutions for Class 10 Maths Chapter 10 - Circles Exercise 10.1
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Exercise 10.1
1.How many tangents can a circle have?
Ans: A circle can have an infinite number of tangents. A circle is made of infinite points and from each point, a tangent can be formed.
2. Fill in the blanks :
(i) A tangent to a circle intersects it in _________ point(s).
Ans: A tangent to a circle intersects it in exactly one point.
(ii) A line intersecting a circle in two points is called a _______.
Ans: A line intersecting a circle in two points is called a secant.
(iii) A circle can have _______ parallel tangents at the most.
Ans: A circle can have two parallel tangents at the most opposite to one another.
(iv) The common point of a tangent to a circle and the circle is called ______.
Ans: The common point of a tangent to a circle and the circle is called the Point of Contact.
3. A tangent PQ at a point P of a circle of radius \[\text{5cm}\] meets a line through the centre O at a point Q so that \[\text{OQ = 12cm}\]. Length of PQ is :
(A) \[\text{12}\]cm
(B) \[\text{13}\]cm
(C) \[\text{8}\text{.5}\] cm
(D)\[\sqrt{\text{119}}\]
Ans: According to the Pythagoras Theorem: \[PQ=\sqrt{\left( O{{Q}^{2}}-\left. O{{P}^{2}} \right) \right.}\]
OQ = \[\text{12}\]cm, OP = \[\text{5}\]cm
Because,
\[PQ=\sqrt{\left( O{{Q}^{2}}-\left. O{{P}^{2}} \right) \right.}\]
\[=\sqrt{\left( {{12}^{2}}-\left. {{5}^{2}} \right) \right.}\]
\[=\sqrt{144-25}\]
\[=\sqrt{119}\]cm.
Hence, (D) is the answer.
4. Draw a circle and two lines parallel to a given line such that one is tangent and the other, a secant to the circle.
Ans: From the Given Figure below,
Let ‘l’ be the given line and a circle with centre O is drawn.
A tangent to the circle from point B is drawn \[\parallel \] to line ‘l’.
CD is drawn \[\parallel \] to line ‘l’ and is the secant.
Conclusion
Vedantu's NCERT Maths Chapter 10 Class 10 Circles Exercise 10.1 Solutions includes detailed solutions and explanations to all questions. We will understand the properties of circles and tangents, especially the relationship between the radius and the tangent at the point of contact. By practising these exercises, we strengthen these concepts and learn the theorems about tangents. Ex 10.1 Class 10 solutions will help you develop an excellent foundation in circle geometry and prepare you for exams.
Class 10 Maths Chapter 10: Exercises Breakdown
CBSE Class 10 Maths Chapter 10 Other Study Materials
Chapter-Specific NCERT Solutions for Class 10 Maths
Given below are the chapter-wise NCERT Solutions for Class 10 Maths. Go through these chapter-wise solutions to be thoroughly familiar with the concepts.
FAQs on NCERT Solutions for Class 10 Maths Chapter 10 - Circles Exercise 10.1
1. What is a circle in Ex 10.1 Class 10?
In Ex 10.1 Class 10, a circle is a shape made up of all points that are the same distance from a fixed point, called the centre. This fixed distance is known as the radius. Circles are fundamental shapes in geometry.
2. What is a tangent to a circle in Ex 10.1 Class 10?
A tangent to a circle is a straight line that touches the circle at exactly one point. This single point is called the point of tangency. The tangent is always perpendicular to the radius at the point of tangency. For more refer Class 10 Circles Exercise 10.1 Solutions.
3. How do you find the length of a tangent from a point outside the circle in Class 10 Maths Ch 10 Ex 10.1?
To find the length of a tangent from an external point, use the Pythagorean theorem, where you can visit Class 10 Maths Ch 10 Ex 10.1 for complete solutions for Pythagorean theorem. Measure the distance from the external point to the centre of the circle, and know the radius. The tangent length can be calculated using these values.
4. What is the point of tangency in Class 10 Maths Ch 10 Ex 10.1?
According to Class 10 Maths Ch 10 Ex 10.1, the point of tangency is the point where the tangent touches the circle. At this point, the tangent is perpendicular to the radius of the circle. This concept is important in understanding circle geometry.
5. Why is the tangent perpendicular to the radius at the point of tangency in Ex10.1 Class 10?
This is a key property of circles. A line drawn from the centre of the circle to the point of tangency is always at a right angle to the tangent. This property helps in solving geometric problems involving circles from Ex10.1 Class 10.
6. What is the importance of understanding tangents in circle geometry Ex10.1 Class 10?
From Ex10.1 Class 10, understanding tangents is crucial because it helps in solving various geometric problems involving circles. Knowledge of tangents aids in proving theorems and understanding circle properties better.
7. How are tangents used in real-life applications in Class 10 Maths Chapter 10 Exercise 10.1?
Tangents are used in many real-life applications, such as in designing wheels, gears, and other circular objects. They are important in engineering, architecture, and navigation for calculating distances and angles.
8. Can a circle have more than one tangent from an external point in Class 10 Maths Chapter 10 Exercise 10.1?
Yes, in Class 10 Maths Chapter 10 Exercise 10.1, a circle can have exactly two tangents from an external point. These tangents are equal in length. This concept is useful in solving geometric problems involving circles.
9. What is the tangent-segment theorem in Class 10 Maths Chapter 10 Exercise 10.1?
The tangent-segment theorem states that the lengths of two tangent segments drawn from an external point to a circle are equal. This theorem is helpful in solving problems related to tangents and circles.
10. How can tangents help in solving problems involving circles in Exercise 10.1 Class 10 Solutions?
Tangents simplify solving problems involving circles by providing relationships between angles and lengths. They are used in various geometric theorems and help in finding solutions to complex problems.
11. What are the key properties of a tangent in Exercise 10.1 Class 10 Solutions?
The key properties of a tangent include touching the circle at one point, being perpendicular to the radius at the point of tangency, and having equal tangent segments from an external point. These properties are fundamental in circle geometry.
12. How do you apply the tangent properties in solving exercises from Exercise 10.1 Class 10 Solutions?
Apply tangent properties by using Exercise 10.1 Class 10 solutions, the relationships between the radius, tangent, and external points. Use the Pythagorean theorem for length calculations, and apply the perpendicularity property for angle problems. Practising these concepts helps in mastering their applications.