**What is a Circle? **

A circle is a closed two-dimensional figure in which the set of all points in the plane are equidistant from a given point called the “center”. Every line passing through the circle forms a line of reflection symmetry. Also, it has rotational symmetry around the center for every angle.

**Circle Definition**

**Circle in Detail**

A circle is a two-dimensional geometric figure characterized by all points equidistant from a central point. Here are some key features.

**Radius (r)**

The distance from the center of the circle to any point on its circumference.

**Diameter (d) **

Twice the radius; the distance across the circle through its center.

**Circumference (C)**

The perimeter or the distance around the circle.

$C = 2\pi r$ or $C = \pi d$.

**Area (A)**

The region enclosed by the circle.

$A = \pi r^2$.

**Some Examples Related to Circles along with their Answers**

**Example 1: Circumference Calculation**

**Question: **If a circle has a radius of 7 cm, find its circumference.

**Answer- ** C = 2π × 7 = 14π cm (or approximately 43.98 cm).

**Example 2: Diameter and Radius Relationship**

**Question:** If the diameter of a circle is 10 units, what is its radius?

**Answer-** The radius is half of the diameter,

**Example 3: Area Calculation**

**Question-** Find the area of a circle with a radius of 3 meters.

**Answer- **

**Example 4: Circle Sector Angle**

**Question- **In a circle with a radius of 8 cm, an angle at the center is 45 degrees. Find the length of the arc it subtends.

**Answer-**

**Example 5: Tangent Line Length**

**Question: **If a tangent is drawn to a circle with a radius of 6 cm from an external point, find the length of the tangent if it makes an angle of 60 degrees with the radius.

**Answer- **Use the tangent line formula.

**Example 6: Inscribed Angle**

**Question:** In a circle, an inscribed angle measures 90 degrees. What is the corresponding central angle?

**Answer-** The central angle is twice the inscribed angle, so Central angle = 2 × 90 = 180 Central angle = 2 × 90 = 180 degrees.

**Example 7: Circles in Nature**

**Question:** The diameter of a circular tree cross-section is 60 cm. What is its circumference?

**Answer-*** C* = *π* × 60 cm.

**Example 8: Circular Pizza**

**Question: **A pizza has a diameter of 16 inches. What is its area?

**Answer-**

**Example 9: Wheel of a Bicycle**

**Question:** If the diameter of a bicycle wheel is 26 inches, what is its circumference?

**Answer- ***C* = *π* × 26 inches.

**Example 10: Circular Coin**

**Question:** The diameter of a coin is 2 cm. Find its radius.

**Answer-**

**Example 11: Circular Mirror**

**Question:** The diameter of a circular mirror is 18 inches. What is its radius?

**Answer-**

**Example 12: Circular Garden**

**Question: **A circular garden has a radius of 5 meters. Calculate its area.

**Answer-**

**Example 13: Circular Swimming Pool**

**Question:** The circumference of a circular swimming pool is 50 feet. Find its radius.

**Answer-**

**Example 14: Concentric Circles**

Question: Draw two concentric circles. Label the radius of the larger circle as *R* and the radius of the smaller circle as *r*. What is the difference in their areas?

**Answer-**

**Read Also**

**Quadratic Equation Definition Formulas and History**

**Some Examples Related to Circles**

**Calculating Circumference**– If a circle has a radius of 5 units, its circumference is 2π × 5

**Diameter to Radius Relationship- **The diameter is always twice the radius.

**Pizza as a Circle- **Pizza slices are often shaped like sectors of a circle.

**Wheel of a Bicycle-** Bicycle wheels are circular.

**Circular Tabletops-** Many tables have circular tops.

**Circular Coins-** Coins are often circular.

**Circular CDs and DVDs- **Optical discs are circular.

**Circles in Nature- **The cross-section of a tree trunk is approximately circular.

**Circular Stamps-** Postage stamps are often circular.

**Circular Traffic Signs-** Many road signs are circular.

**Circular Clocks-** Clock faces are typically circular.

**Ferris Wheels- **The shape of Ferris wheels involves circles.

**Target Boards- **Targets used in shooting sports are circular.

**Circular Moon-** The moon appears circular.

**Circular Buttons- B**uttons on clothing can be circular.

**Circular Plates- **Plates are often circular in shape.

**Circular Mirrors-** Mirrors are often circular.

**Circular Hula Hoops- **Hula hoops are circular toys.

**Circular Water Ripples-** When you drop an object into water, it creates circular ripples.

**Circular Watch Faces- **Watch faces are typically circular.

**Tires on Cars-** Car tires are circular.

**Circular Lenses- **Eyeglass lenses are often circular.

**Circular Coffee Cups- **The tops of coffee cups are circular.

**Circular Doilies- **Decorative doilies are often circular.

**Circular Garden Pots-** Many plant pots have a circular shape.

**Circular Cookies- **Cookies are often circular.

**Circular Stickers- **Stickers can be circular in shape.

**Circular Steering Wheels- **Steering wheels are typically circular.

**Circular Buttons on Websites- **Online buttons are often circular.

**Circular Frisbees-** Frisbees are circular flying discs.

**Circular Rings- **Rings can be considered as circles.

**Circular Platters- **Serving platters are often circular.

**Circular Coins- **Many coins are circular.

**Circular Earrings- **Earrings can have a circular design.

**Circular Street Manholes-** Manhole covers are often circular.

**Circular Cookies- **Cookies are often circular.

**Circular Ice Cream Cones- **Ice cream cones have a circular base.

**Circular Pies-** Pies are often circular in shape.

**Circular Stairs- **The shape of staircases can involve circles.

**Circular Buttons on Electronic Devices-** Buttons on devices like smartphones can be circular.

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