SLC S23 Week3 || Geometry with GeoGebra: Circles and its elements

Hello everyone.

It's another week for us to contest and equally share our amazing entries on GeoGebra. It's week 3 of the learning challenge. And This time we will be working with circle geometry. Here is my entry post.

1.

Construct a circle and show its main elements.

A circle is a shape search that all points on its path are equal distance from a single point known as the center. Circle elements constitute point or lines that are attributed to a given cycle.

This represents a point from the center of the circle to any point on the circumference of that circle.

To begin with, we start by creating our cycle under the circle tool. Here we are going to select a cycle with Center. From which we draw out a cycle of our desire size.

Under the line tools, We select a line segment from the center to any point on the circumference of the circle for

If we move the Radius about the circle, we will notice that the Points will stay exactly on the circumference.

The diameter is a straight line which device the circle into two equal halves. It's passed through the center of the circle and equally constitute the sum of the two radius of the circle to from the diameter.

An arc Is the measure of the lungs between two points on the circumference of the circle.

This is the total distance measured round the circle. It is usually given by the formula. 2πr.

A segment Is the portion of the area between a chord and an arc of the circle.

This is a line that connects two points on the circumference of the circle but does not pass through the origin or Center. It is often referred to us the secant line.

This is a fragment of the circle, And it constitute two radius and an arc. The portion between the circle radius and the arc is noon as a sector.

This is a line which touches the circle at one point on the circumference, and it is perpendicular to the radius of the circle. This is a unique feature which makes a line to be tangent to a circle. Perpendicularity.

** General properties**

2.

Construct circle O and chord AB on it. On this chord, construct the central angle. Place point D on the circle, and construct the inscribed angle ∠ADB on the same chord AB. Show the degree measures of these two angles (∠AOB and ∠ACB). Move point D. What conclusion can be drawn?

To begin with, we start by selecting our circle, And giving its center O. To proceed, we add another point be in the sector and form a chord AB.

Using the line segment, we construct two lines from A and B to join at the center O. We use the angle tool to measure the angle AOB.

On the same side, on the circumference of the circle, we at another Point D and construct two lines, To meet at Point A and point B. From here we measure the angle. ADB.

Note:

• It can be observed there as we move the point D on the circumference, it remain unchanged unless we flipped it over the chord.

• The second point to draw from here is that the angle? ADB, it's exactly half the Angle AOB. Which is theorem 1 for properties of circles theorem.

3.

Construct segment CD. On this segment CD, as the diameter, construct a semicircle. Take point F on the semicircle and form the angle ∠CFD. Move point F. What conclusion can be drawn?

Starting off, We Begin by in certain points A and B, renaming it C and D. Under the cycle tools. We Select the semicircle option, and then Construct a semicircle from point C to D.

On the circumference of the semicircle, we at the point F And construct a triangle.<CFD using the line segment tool.

Using the angle tools, we measure the angle.<CFD.

Note:

• Observing, by measuring the angles, Angle CFD it's exactly 90°. Hence indicating that ∆ CFD is a right angle triangle.

• Another point to draw from here is that the line CF is perpendicular to The line DF.

4.

Construct triangle ABC. Construct two circles – the inscribed and circumscribed circles. (Do not use the "circle through three points" tool for the circumscribed circle.)

To begin with, We start by creating our triangle ABC using the polygon tools. From here, we use the angle bisector for any two of the children sites.

From here we intersect the bisectors, and followed by adding a perpendicular line and intersecting it with one side.

We didn't use the line segment to draw the radius of the circle. From here, we go another circle tools And two circle with Center, Take it to our intersection point G And inscribe our circle and extend it to the edges. Our plane will fall on the same point as our radius.

From here, I will hide the bisector lines and then multiply the line to my taste. Below is an illustration of our task.

Moving on to circumscribed circle, we start by drawing perpendicular bisectors on the triangle choosing any of the two sides. After which, we intersect the points, every locate these points using the line segment after which are hidden.

From here, we can draw our circle and extend it to the vertices of the triangle. Thereafter, our circumscribe circle is formed.

5.

Use your imagination – construct something similar to this. Do you know what it is called?

Image 1:.

Looking at image one, one can see that the two internal circle's touch externally. The two circles combine Dodge internally with the general circle. When this is analyzed, we can see that the point on the second friends of the two circle is a glide which helps to move the two circles in One direction once the other One is moving in the opposite direction.

Equally the antenna circles intersect with the externals major cycle. 42 seconds to be able to increase and decrease at intervals, one can draw conclusion that the outer point on the circle of this radius is exactly the same for both of them. That is the external point let's say B for circle one Is exactly on the same point as the external point on the second with a point on the circumference B'.

Let's try to replicate this and see how it goes.

To begin with, I started by creating the major circle using two semi circles.

After which I proceed by creating another Set of semi circles I'm making sure their points on the circumference intersects with a major circle. Once this is complete, our circle Can move and it gets observed that When one increased in radius. The other one reduce equally.

Image 2.

For image 2, It is observed that there are two Major circles, One is inscribed and the other one is circumscribed which is the major sector. Now intersect with the circumscribed circle, While using the edge of the triangle as the tangent line.

Let's see how we can do this. Yes, we said by creating our triangle and inscribing a circle. We have already seen the various steps To produce and inscribed circle. Same as circumscribed. So we will do that right away and see how Three smaller circles.

Our inscribe circle is complete, let's see how to produce the circumscribed circle.

Conclude, I am so happy to have participated in this fun challenge. I learn a lot From the process and I am so happy I was able to carry majority of the task well.

I invite the following persons to join me participate.
@chant, @fombae, @simonnwigwe