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The word "bisector" means to divide a sector into two equal parts. Wherever you hear the word bisector in maths, that means you need to divide something into two equal halves. Some of the examples of bisector are perpendicular bisector, triangle bisector, line bisector, etc. One of those examples is angle bisector, so the question is what is an angle bisector and how do we deal with it? Let's find it out.
Angle Bisector
The angle bisector is the line that passes through the vertex of the angle and divides it into two equal parts. Consider the diagram below:
There is an angle between two lines. That angle is divided into two halves and that is represented by a green line. The green line also indicates that both of its sides are also equal. Basically, the green line is the middle point of both lines. To find bisectors whether it is a perpendicular bisector or angle bisector, we require geometrical tools. These tools are 100% precise and used to find accurate bisectors. There are so many tools used for bisectors but in this resource, we will tell you what tools you require in order to find the angle bisector.
Tools Requirement
To find an angle bisector, you will be needing:
- Protector
- Geometrical Compass
- Ruler
These three are the main tool that you need for an angle bisector. Now, let's move to how to draw an angle bisector.
Drawing Angle Bisectors I
In this case, you have an angle between two lines and you are asked to find the angle bisector. Below are the steps.
1Draw an arc corresponding to the angle by using the vertex as the pivot point for the compass. Make sure the pivoting point is the same for both lines, use a ruler for uncertainty.
2From both ends of the drawn arc (where the arc meets the arms of the angle) draw equal arcs from each of the intersecting points.
3Draw a straight line from the point of intersection of the arcs and the vertex of the angle.
Drawing Angle Bisectors II
Another method for drawing angle bisectors is called the circular method. This method might be a little time consuming but it is more accurate and it has less probability for error. Let's talk about the steps:
1.Draw a circle of any size using the vertex of the angle as the centre of the circle.
2.At the point of intersection of the circle and the arms of the angle, draw two smaller circles with the same radius.
3.The line that passes through the vertex of the angle and one of the points of intersection of the circles is the angle bisector.
Incenter
The angle bisectors of a triangle are each one of the lines that divide an angle into two equal angles.
1.Find the centre of every side of the triangle and mark that point.
2.Draw a line from the vertex of every side to the opposite side intersecting the centre point of that side. Do it for all sides.
3.The point where all three lines are intersecting is the centre of the triangle.
The incenter is the point of intersection of the three angle bisectors. Furthermore, it is also the centre of the circle inscribed in the triangle.
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I’m just curious if the area between the polygon and the circumscribed circle has a name.
https://www.superprof.co.uk/resources/academic/maths/geometry/plane/orthocenter-centroid-circumcenter-and-incenter-of-a-triangle.html