**Circle**

A circle is a closed, two-dimensional geometry with a curving side whose ends meet to create a round shape. The name “circle” comes from the Latin word “circulus,” which meaning “a small ring.” You can read more about the concept of a circle, the formulas that apply to circles, the many parts of a circle, and practise some circle problems on this page.

**What is Circle?**

A circle is a two-dimensional object that consists of a collection of points spaced apart by a fixed point (centre) on the plane at a fixed distance (radius). The radius is the fixed distance between the points and the origin, and the centre or origin of the circle is the fixed point. The following illustration shows the fundamental elements of a circle, such as the centre, radius, and diameter.

**Parts of a Circle**

It is essential to comprehend a circle’s many constituent parts in order to comprehend its qualities. The following are some crucial components of a circle:

**Circumference:** also referred to as a circle’s perimeter, is the measurement of a circle’s outermost point.

**Radius: **The radius is the separation between a circle’s centre and any point on its edge. There are indefinitely many radii on a circle.

**Diameter:** A straight line connecting two locations on the circle’s edge passes through the centre. It’s important to remember that a circle can have more than one diameter, but they must all:

- Traverse the centre

- Keep lines straight

- Two separate points opposite to each other must touch the edge of the circle

It’s crucial to comprehend the various parts that make up a circle. Here are some of a circle’s fundamental components:

**Chord: **A chord is a line segment that crosses the circle’s perimeter at two different locations. The diameter, which runs through the centre and splits the circle in half, is the longest chord in a circle.

**Tangent:** A tangent is a line that crosses a circle only once and is otherwise outside the circle.

**Secant: **A secant is a line that crosses the arc or circumference of a circle at two different points.

**Arc: **An arc is a segment, or piece, of a circle’s circumference.

**Segment: **A segment in a circle refers to the region enclosed by a chord and the corresponding arc. There are two types of segments: minor and major segments.

**Sector: **A sector of a circle is the area enclosed by two radii and the corresponding arc. There are two types of sectors: minor and major sectors.

**Properties of Circle**

It’s crucial to comprehend the various parts that make up a circle. Here are some crucial components of a circle:

The following are some of the crucial characteristics of a circle:

- If the radii of two circles match, they are said to be congruent.

- The longest chord is a circle’s diameter.

- In the centre of a circle, equal chords subtend equal angles.

- The chord is divided in half by the radius drawn perpendicular to it.

- Circles with various radii can resemble one another.

- Rectangles, trapezoids, triangles, squares, and kites can all be encircled by circles.

- A square, triangle, and kite can all contain a circle.

- Equal lengths are shared by the chords that are equally spaced from the centre.

- Zero metres separate the circle’s centre (longest chord) from its diameter (shortest chord).

**Circle Formulas**

A circle’s area is equal to r2 square units.

A circle’s circumference is equal to 2r units.

A circle formula’s circumference can also be expressed as d.

Where,

Radius 2 Diameter

d = 2r

Here, “r” stands for a circle’s radius.

**Circle Solved Problems**

**Question 1**

**Find the distance travelled in 20 revolutions by a 56 cm diameter wheel.**

**Solution:**

56 cm is the wheel’s radius.

Wheel circumference = 2r = 2 22/7 56 = 352 cm.

20 revolutions equal 20 x 352 which is 7040 cm or 70.40 metres.

**Question 2**

**Find the amount of paper that remains after cutting a circle out of a square of paper with a side of 7 cm if the circle’s diameter is equal to the square’s side.**

**Solution:**

7 cm is the square’s side.

7 cm is the circle’s diameter.

Circle radius: 7/2 cm

The amount of square paper after the circle has been cut out equals the amount of the circle.

= side2- (𝜋r2) = 72- [22/7 × (7/2)2]

= 49 – 38.5

= 10.5 cm2

**Question 3**

**A circle with a diameter of 10 cm should have the area and circumference determined.**

**Solution:**

Given:

The diameter is 10 cm.

We are aware that diameter equals two times the radius.

Consequently, radius, r = d/2.

r = 10/2 = 5

The radius is thus 5 cm.

A circle’s area is equal to r2 square units.

A = 3.14 x 5 x 5

Where ,

π = 3.14

A = 3.14 x 25

A = 78.5 cm2

Consequently, a circle’s area is 78.5 square units.

A circle’s circumference is equal to 2r units.

C = 2 x 3.14 x 5

C = 10 x 3.14

C = 31. 4 cm

**Frequently Asked Questions on Properties of Circle**

**What feature does a circle have?**

A circle is a geometric shape made up of a group of points that are all equally distant from one another; this common point is known as the circle’s centre, and the distance from the centre is known as the radius of the circle.

**What prerequisite exists for the circles’ similarity?**

No matter how different the radii of the circles are, they are all comparable.

**What prerequisites must exist for circles to be congruent?**

The circles are congruent if the radii of the given circles are equal.