Out of all the geometric shapes and figures, the circle is a fascinating form present around us. The pizza, coins, the sun are all circular in shape (two-dimensional). Just a few important things in our lives that are circular in shape. And have you ever thought about how many sides a circle has? Let us study what is a circle in detail.

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## What is a Circle?

AÂ **circleÂ **is a shape wherein all points have the same distance from the centre. Few real-world examples include a wheel, dining plate, coin etc. Drawing it properly isnâ€™t easy with a running hand. The availability of a compass (a geometric tool) is preferred by most people, be it at school or at the workplace.

*2D drawing of a sphere is a circle*

## Important Terms Related to Circle

We know what is a circle. But what are the parts of a circle? Here are a few important terms that make up for the parts of a circle.

**Diameter:**The diameter is a line which is drawn across a circle passing through the centre.**Radius:Â**The distance from the middle or centre of a circle towards any point on it is a radius. Interestingly, when you place two radii back-to-back, the resultant would hold the same length as one diameter. Therefore, we can call one diameter twice as long as the concerned radius.**Area of Circle:Â**In a circle, the area can be stated as Ï€ times the square of the radius. It is, A = Ï€ r^{2}. Taking into consideration the diameter: A = (Ï€/4) Ã— D^{2}**Chord:Â**A line segment that joins two points present on a curve is the chord. In geometry, the usefulness of a chord is focused on describing a line segment connecting two endpoints which rest on a circle.**Tangent & Arc:Â**A line which slightly touches the circle on its travel to a different direction isÂ**Tangent**. On the other hand, a part of the circumference is anÂ**Arc**.**Sector & Segment:Â**A sector is a part of a circle surrounded by two radii of it together with their intercepted arc. The segment is that region which is enclosed by a chord together with the arc subtended by the chord.

**Download Mensuration Cheat Sheet PDF Below**

**Properties of the Circle**

- Circles with equal radii are congruent.
- Also, the circles with different radii appearÂ to be similar.
- The chords that are equidistant from the centre are of the same length.
- All points on the circle are equidistant from the centre point.
- The longest chord in the circle is the diameter.
- A diameter of a circle divides it into two equal arcs. Each of the arcs is s a semi-circle.
- If the radii of two circles are exactly the same value, then the circles are congruent.
- Two or more circles that have different radii but the same centre are concentric circles.

## Solved Questions

**Question 1.Â Three circles are mutually tangent externally Their centres form a triangle whose sides are of lengths 3, 4 and 5 The total area of the circles (in square units) is**

**9Â Ï€****16Â Ï€****21Â Ï€****14Â Ï€**

**Answer :** D. Let the respective radii of the circles be a, b and c. then,

a + b = 3Â Â Â Â Â Â Â (1)

b + c = 4Â Â Â Â Â Â Â (2)

c + a = 5Â Â Â Â Â Â Â (3)

Adding all three,

a + b + c = 6Â Â Â (4)

From the above equations, we have

c = 3, a = 2, b = 1

Now the area of three circles =Â Ï€ (1Â²) +Â Ï€ (2Â²) +Â Ï€ (3Â²) =Â Ï€ + 4Ï€ + 9Ï€ = 14Ï€

**Question 2.Â A horse is tethered by a rope 10 m long at a point. Find the area of the region where it can graze (Ï€ = 3.14)**

**Answer :** The area of the region the horse can graze is circular with a radius equal to the length of the rope.

Area of the circle isÂ Ï€rÂ²

= 3.14Â Ã— 10Â²

= 3.14Â Ã— 100

=314

Hence the area of the region the horse can graze is 314cmÂ²

**Question 3: Give the definition of circle in math?**

**Answer**: A circle refers to a round shape that is two-dimensional in nature. All points on the edge of the circle happen to be at the same distance from the centre. The diameter of a circle is such that it is equal to twice its radius. A Circle is a shape that lacks any edges or corners. This shape is made up of a curved line.

**Question 4: Can we say that a circle is a polygon?**

**Answer:** Polygon refers to a closed plane figure involving three or more straight sides. According to this definition of polygon, a circle is not a polygon. This is because a circle lacks straight sides.

**Question 5: What is meant by pi?**

**Answer:** Pi is a number that turns out to be approximately 3.142. This value is any circleâ€™s circumference divided by its diameter. The Greek letter Ï€ denotes the value of pi.

**Question 6: Can we say that the circle has an end?**

**Answer:** A circle is basically a curve that is characterized by an infinite number of points which always maintain the same distance from the centre point. In other words, a circle is devoid of any endpoint.

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