MIE: Mensuration and Geometrical Properties of Circle

By: Lina Indra

What we have learned so far…

The property of circle:

As we have known, a circle consists of:

  • Diameter
  • Radius
  • Circumference
  • Area

Except for that, a circle consists of other properties. Some of them are:

  • Chord
  • Segment
  • Sector
  • Arc
  • Tangent

 1

Pic 1.1

As we have known from the picture, a segment and a sector is the area of the shaded part while the arc and the circumference is the line that made up the circle.

To calculate the area in a sector, this following formula will be able to make you find the area.

As for the segment, this will be a little hard. First, you will have to find the sector area of the segment that you wanted to find. Next, draw a line to make an equilateral triangle and find the triangle’s area. Then, subtract the sector are with the area of the equilateral triangle and you will get the area of the segment.

The same goes for the arc. As we have known, arc is also a part of the circle’s perimeter so the formula can be written like this:

Next, we’re going to talk about The properties of Circle.

As each of us knows, a circle is a very special shape in geometry. With its special shape, it has several special properties that have been proved by mathematician.

  1. The angle  is equals to two times of angle.

This property is only valid when the line that was drawn reaches or was at the center of the circle. And also this property is valid when the longer line that is angle A touches the circumference of the circle.

2Pic 1.2

2. Any angle that was drawn from the two endpoints of a diameter of a circle will form a 90 degree. Note that this property is only valid when the line is drawn from the two endpoints of a circle Diameter.

3

Pic 1.3

3. Any triangle that was located at the very same segment will have the same number of angle as in the picture. Where   . This property is only valid when the triangle is located in the same segment and the line used to form the said triangle must reach the circumference of the triangle.

4

Pic 1.4

 

Additional Properties of a Circle

Besides the properties known from the above three, there are actually several other properties that the circle has, but this time, the shape formed inside the circle is not triangle, but it was a rectangular.

Thus, this property is called as The Opposite Segment. In this property, the shape drawn must be a rectangular shape. It states that any angle inside the rectangular shape, if being summed up with the angle that was located at the opposite way (For ex. Up and down) will be equal to.

As can be seen from the picture below, the property can be applied to the angle with the same color so if  the same also applies with the angle with the color blue.

5

Pic 1.5

Tangent

Another name of a line that interacts with a circle is called a tangent. It was different from all the lines that we have learned this far. Previously, we have learned about the line that crosses the area of the circle which is called Diameter, Radius, Secant and Segment. This time, instead of located inside the area of the circle, this line crosses the circle from outside, but it somehow, touches one point of the circumference of the circle.

6

Pic 1.6

The special thing about this line, is that when a line (Radius) is drawn from the center of the circle towards the tangent, it will create an angle where the size of the angle is equal to 90 degrees.

This is all that we have learned so far.

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