Circles Class 10 Notes: Chapter 10

A circle is a closed shape with a set of points in a plane which are at a specific distance from the center. This specific distance is known to be the radius of a circle. It is important to learn all the details about a circle along with some important points associated with it like locus, a circumference of a circle, area, etc. 

Circles class 10 notes for chapter 10 provided here are an extremely important resource for the students studying in CBSE class 10. Students can use these revision notes to understand the concepts covered in this chapter and revise the concepts quickly. The following concepts are covered under this section:

Circles for Class 10

Class 10 Mathematics Notes Chapter 10 Circles

Class 10 Circles Notes are based on parts of circles, circle tangents and its theorems. The important definitions, facts and formulas for each concept are also provided to make revision faster and easier. BYJU’S Experts have consolidated some of the most important questions which could feature in an exam.

Circle Definition – Collection of points in a plane which are located at a fixed distance.

Centre Point – Fixed point located at centre.

Radius – Constant distance from centre to circumference.

Diameter – Longest segment of the circle passing through the centre.

Circumference of circle – The total distance around the circle.

Chord of a circle – Line segment joining two points on the circumference.

Sector of a circle – The region enclosed by two radii and corresponding arc.

Segment of the circle – The region bounded by a chord and corresponding arc.

Tangent to a Circle –  A tangent is defined as a line that intersects the circle at only one point. For any point on the circumference of a circle, there exists one and only one tangent to a circle at that point.

Secant of circle – A line that intersects the circle exactly at two points. 

Tangent of a Circle Theorem

Amongst all the Circles class 10 theorems, there are two tangents of a circle theorem which are:

  • The tangent at any point of a circle is perpendicular to the radius through the point of contact.
  • The lengths of tangents drawn from an external point to a circle are equal.

Let’s learn about these two theorems with proofs.

Theorem 1: The tangent at any point of a circle is perpendicular to the radius through the point of contact. The prove of this theorem is also given below.

Circles For Class 10

Theorem 2: The lengths of tangents drawn from an external point to a circle are equal. Below given is the proof of theorem 2.

Circles For Class 10

Example Problems

Circles For Class 10

 

 

Practice Questions on Circles Class 10

Practice these questions on Circle for a better understanding of this topic.

  1. The tangents drawn at the ends of a diameter of a circle are parallel. Prove.
  2. Find the radius of a circle if the length of a tangent from a point X at a distance 5 cm from the centre of the circle is 4 cm.
  3. Prove that a parallelogram circumscribing a circle is always a rhombus.

Related Concepts

Keep visiting BYJU’S to get more such notes and study materials for class 10 exam.

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