Circle – Definition, Formulas, and Applications

 Circle – Definition, Formulas, and Applications

1. Definition

A circle is the set of all points in a plane that are at a fixed distance (radius) from a fixed point (center).

---

2. Important Terms

Center (O): The fixed point.

Radius (r): Distance from center to any point on the circle.

Diameter (d): Twice the radius. 

Circumference (C): The perimeter of the circle.

Chord: A line joining two points on the circle.

Arc: A part of the circumference.

Sector: A region bounded by two radii and an arc.

---

3. Formulas

1. Circumference:

C = 2\pi r

A = \pi r^2

L = \frac{\theta}{360^\circ} \times 2\pi r

A_{\text{sector}} = \frac{\theta}{360^\circ} \times \pi r^2

---

4. Applications

In wheels, coins, clocks.

For calculating distances in circular tracks.

In geometry problems and engineering designs.

---

5. Example Problem

Q: A circle has radius . Find its circumference and area.

Solution:

C = 2\pi r = 2 \times 3.14 \times 7 = 43.96 \text{ cm}

A = \pi r^2 = 3.14 \times 7^2 = 153.86 \text{ cm}^2 

---

✍ Written by: Sarthak Prakash Patil