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Basic Geometrical Ideas

Circle

Out of all the geometric shapes and figures, the circle is a fascinating form present around us. Be it the sun, moon and even a bottle cap, circular objects are quite common. Let’s try to understand its proper definition of circle and circle area together with the various aspects that are associated with geometry.

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Definition of Circle ( Circle Formula )

A circle is a shape wherein all points have the same distance from the center. Few real-world examples include a wheel, dining plate, coin etc. Drawing it properly isn’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.

circle area

Important Terms Related to Circle 

Diameter

The diameter can be termed as a line which is drawn across a circle passing through the center.

Radius

The distance from the middle or center 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.

Circle Area

In a circle, the area can be stated as π times the square of the radius. It is written as: A = π r2. Taking into consideration the Diameter: A = (π/4) × D2

Chord

A line segment that joins two points present on a curve is called as 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

A line which slightly touches the circle on its travel to a different direction is Tangent. On the other hand, a part of the circumference is an Arc.

Sector & Segment

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.

Common Sectors

In geometry, Quadrant and Semicircle are known as two special versions of a sector.

  • A circle’s quarter is termed as Quadrant.
  • Half a circle is known as a Semicircle.

Properties and Key Aspects

Focusing on geometry, there are numerous facts associated with circles. Further, the relation of it to straight lines, polygons, and angles can also be proved. All of these facts together are properties of the circle. Let us try to learn the primary properties in order to enhance our knowledge.

  • Circles holding equal radii are known to be congruent.
  • To your surprise, circles with different radii are seen as similar.
  • In a circle, the central angle that intercepts an arc is known to be double to any inscribed angle which intercepts the same arc.
  • The chords that are equidistant from the center are known to be of the same length.
  • A radius perpendicular to a particular chord does bisect the chord.
  • The tangent is always at right angles to the radius considering the point of contact.
  • Two tangents which are drawn on a circle from an exterior point are equal in length.
  • The circumference of two diverse circles is proportional to the corresponding radii.
  • The angle subtended at the circle’s center by its circumference is known to be equivalent to four right angles.
  • Arcs associated to the same circle are termed proportional to their corresponding angles.
  • Equal chords hold equal circumferences.
  • Equal circles hold equal circumferences.
  • Radii linked to the same or equal circles are known to be equal.
  • The longest chord is the diameter.

Question For You

Question 1. Calculate the area of a circle having radius 1.2 m.

Answer : The area here can be calculated using the formula, Area = πr2
Therefore, A = π × 1.22
= 3.14159… × (1.2 × 1.2)
= 4.52 (to 2 decimals).

Question 2: How to find the area of the circle?

Answer: The formula for finding the area of the circle is πr2. Moreover, you can find the area of a circle by multiplying the value of pi that is 3.14 or 22/7 by the square of the radius. However, in place of radius diameter of a circle is mentioned in the question then half it as the radius is half of the diameter.

Question 3: Is the circumference of a circle squared?

Answer: Usually, we can define pi as the ratio of the circumference of a circle to its diameter, hence the circumference of a circle is pi times the diameter, or 2 pi times the radius. So, this provides a geometric proof that the area of the circle really is πr2.

Question 4: Give a simple definition of a circle?

Answer: It refers to a round 2D shape in which all the points on the edge of the circle are at the same distance from the center. Moreover, the diameter of a circle is equal to twice its radius. In addition, the circumference of a circle is the line that goes around the center of the circle.

Question 5: Define the radius of a circle?

Answer: It refers to the distance between the centers to any point on its circumference. The simplest way to find radius is to half the diameter.

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