What is Circle Definition Class 10: Complete Guide for NCERT Maths

Basic Definition of a Circle in Class 10 Mathematics

A circle is defined as the set of all points in a plane that are at a fixed distance from a fixed point. This fixed point is called the centre of the circle, and the fixed distance is called the radius.

• Centre: The fixed point inside the circle, usually denoted as $O$.
• Radius: The distance between the centre and any point on the circle, denoted as $r$.

Mathematically, if $O$ is the centre and $P$ is any point on the circle, then:

$$OP = r$$

where $r$ is constant for a given circle.

This definition forms the foundation of the chapter "Circles" in Class 10 NCERT Mathematics.

Important Terms Related to Circles

To fully understand what is circle definition class 10, you need to know these important terms:

• Radius ($r$): Distance from the centre to any point on the circle.
• Diameter ($d$): A chord passing through the centre; $d = 2r$.
• Chord: A line segment joining two points on the circle.
• Arc: A part of the circumference between two points.
• Circumference: The complete boundary of the circle.
• Sector: The region enclosed by two radii and an arc.
• Segment: The region enclosed by a chord and an arc.

Knowing these terms helps in solving geometry problems involving circles.

Key Properties of a Circle

Understanding the properties of a circle is crucial for Class 10 exams. Here are some key properties:

• All radii of a circle are equal.
• The diameter is the longest chord.
• The perpendicular from the centre to a chord bisects the chord.
• Equal chords are equidistant from the centre.
• The angle subtended by a diameter at the circumference is a right angle.

These properties help in proving theorems and solving problems related to circles.

Formulas Related to Circles for Class 10 Students

Here are important formulas you must remember:

Example:

If the radius of a circle is 7 cm, find its circumference and area.

• Circumference: $C = 2 \times \pi \times 7 = 14\pi$ cm
• Area: $A = \pi \times 7^2 = 49\pi$ cm²

These formulas are frequently tested in CBSE Class 10 exams.

Solved Example on Circle Definition and Properties

Example:

Find the length of a chord of a circle with radius 10 cm if the distance from the centre to the chord is 6 cm.

Solution:

Let the chord be $AB$ and the centre be $O$. Let $OM$ be the perpendicular from $O$ to chord $AB$.

Given:

• $OA = 10$ cm (radius)
• $OM = 6$ cm (distance from centre to chord)

Since $OM$ bisects the chord $AB$, let $AM = MB = x$ cm.

Using Pythagoras theorem in triangle $OMA$:

$$OA^2 = OM^2 + AM^2$$ $$10^2 = 6^2 + x^2$$ $$100 = 36 + x^2$$ $$x^2 = 64$$ $$x = 8$$

Length of chord $AB = 2x = 16$ cm.

This example shows how circle properties and definitions are applied.

Difference Between Circle and Other Shapes

Understanding how a circle differs from other shapes is helpful:

This comparison clarifies the unique property of circles in geometry.

Tips to Master the Circles Chapter for Class 10 Exams

To excel in the Circles chapter:

• Memorize key definitions and formulas.
• Draw neat diagrams for every problem.
• Practice NCERT textbook examples and exercises.
• Understand theorems instead of rote learning.
• Solve previous year CBSE questions.
• Revise regularly to retain concepts.

Following these tips will boost your confidence and performance in the Class 10 Mathematics exam.