SLC S23 Week3 || Geometry with GeoGebra: Circles and its elements
The following are the elements of a circle:
Center:
This is the point inside the circle and is equidistant from every point on the circle.
Radius:
This is the distance from the center of the circle to any point of the circle.
Diameter:
This refers to the longest distance across the circle, that passes through the center of the circle thereby dividing it into two equal halves (semicircle)
Circumference
This is the distance around the circle.
Arc:
This is a part of or two points on the circle's circumference other than the center.
Sector:
This is a combination of two radii and an arc otherwise described as a region of the circle enclosed by two radii and an arc.
Chord:
This is a line segment connecting two points on the circle without crossing the center of the circle.
Segment
This is the part of a circle between its circumference and a chord usually other than the diameter.
Tangent:
This refers to a line that touches the circle at precisely one point.
Secant:
This is a line intersecting a circle at two points.
1. Construct a circle and show its main elements. |
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From the above diagram,
A is the center of the circle.
Line AB is the radius.
Line CD passing through A is the diameter.
The two radii AB and AC alongside the arc BC form the.
Line EF is the chord while joining it with the arc EF through G will form the segment.
Line IJ touches the circle at exactly the point H and therefore is the tangent
Line KL, which intersects the circle at two points E and G, is the sectant.
The circumference which is the distance around the circle encompasses the points CBHDFGE
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? |
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I constructed a circle O with chord AB, after which I constructed the central angle measuring 106.8⁰
Next, I placed point D on the circle with which I constructed the inscribed angle ABD measuring 53.4⁰
From the image below, the central angle ∠AOB measures 106.8⁰ while the inscribed ∠ADB measures 53.4⁰
https://youtube.com/shorts/HNX3T6xFUTM?si=l1jCcmw-gD9-NT7a
Drawn Conclusion
Moving point D through the circumference of the circle, the value of the angle changes from 53.4⁰ to 126.6⁰ as soon as it crosses the chord and enters the arc in the segment.
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? |
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Using the appropriate tool, I constructed the segment CD. Thereafter, I constructed a semicircle.
Next, I proceeded to add point F on the semicircle after which the ∠CFD was constructed which measures 90⁰
https://youtube.com/shorts/q9C6Mpno1fw?si=BEtWwbU8m71vu3Ym
Drawn Conclusion
From the above, we can conclude that the value or measure of the angle ∠CFD remained the same irrespective of its position on the semicircle.
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.) |
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In constructing the inscribed circle, I first constructed triangle ABC using the polygon tool. Next, I introduced my bisectors to locate the center bisection of the triangle and at least one bisection on either of the three sides.
After introducing the bisection lines, I put a point D on the center intersection and the a point E on the intersection on line BC. Afterwards, using circle with center through I drew a circle from the center D to point E which is seen to have intersected the three sides of the triangle.
Following the same steps as in inscribed, I constructed triangle ABC and also introduced two bisector lines to generate the center of the circle to be constructed.
Following the introduction of the bisecting lines, I point a point D on the intersection of the bisectors thereafter drew a circle from this point D to intersect the three vertices of the triangle.
https://youtube.com/shorts/SgBjfpJhO4o?si=24hj1Cgi9n3djGZp
5. Use your imagination – construct something similar to this. Do you know what it is called? |
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From the above, while circle 2 intersects circle 1 and circle 3, circle 1 and circle 3 have external touch.
In this, circle 2 is inscribed in circle 1 and touches it internally. Circle 1 and circle 3 intersects while circle 2 and circle 3 has no intersection or touch.
Thank you
Inviting @suksess, @ninapenda, and @ruthjoe
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