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we bring forth to you the HISTORY of circles (:
The circle has been known since before the beginning of recorded history. It is the basis for the wheel, which, with related inventions such as gears, makes much of modern civilization possible. In mathematics, the study of the circle has helped inspire the development of geometry and calculus.
Early science, particularly geometry and Astrology and astronomy, was connected to the divine for most medieval scholars, and many believed that there was something intrinsically "divine" or "perfect" that could be found in circles.
Some highlights in the history of the circle are:
* 1700 BC – The Rhind papyrus gives a method to find the area of a circular field. The result corresponds to 256/81 as an approximate value of π.
* 300 BC – Book 3 of Euclid's Elements deals with the properties of circles.
* 1880 – Lindemann proves that π is transcendental, effectively settling the millennia-old problem of squaring the circle.
Euclid
~325 BC - 265 BC
The Elements
Many geometrical axioms and propositions
Wrote all this in 300 BC!
Java applets: Euclid’s Elements, Book III, Proposition 1
SOURCE:www.wikipedia.com
*Circle & God:
Early science,particularly geometry and astronomy/astrology,was connected to the divine for most medieval scholars.The compass in the13th century manuscript is a symbol of God's act of creation,as many believed that there was something intrinsically "divine" or "perfect" that could be fund in circles.
In ancient Rome,circles were worshipped as they were thought to be divime and holy
There should be no need for introduction again here. So well lets get to the main aim of this blog: for you all to better understand the properties of circles.
Hope the information here will be useful and if you do have any queries,feel free to tag at our SWEET LIL TAGBOARD and we will try to attend to it as soon as possible.
Most importantly,we hope you have enjoyed your stay here.(:
Paper
PROPERTIES OF CIRCLES
angle properties of circles:
(1) Angle at Centre,
(2) Angle in Semicircle,
(3) Angles in Same Segment,
(4) Angles in Opposite Segments.
symmetrical properties of circles:
(1) Straight line perpendicular to chord
(2) equal chords equidistant from centre
angle in opposite segments of a circle
tangents in a circle:
(1) Tangent perpendicular to radius
(2) Tangent from an external point
Entries
Stories of C-I-R-C-L-E-S //
Blogged on : Saturday, July 18, 2009
Blogged at : 4:58 AM
Did you know:
Properties of circle can be divided mainly into the following two parts
- Symmetrical properties of circle
- Angle properties of circle
Symmetrical properties of circles
Chords of a circle
Chord is a straight line that touches the circumference of the circle at any two points.
- Perpendicular bisector of a chord (perpendicular bisector of chord)
The perpendicular bisector of a chord of a circle passes through the centre of circle.
- Perpendicular from the centre of a circle to a chord bisects the chord (perpendicular from centre bisects chord)
- Equal chords of a circle are equidistant from the centre of a circle (Equal chords, equidistant from centre)
- Tangents to a circle
Tangent at a Point
Tangent from anExternal Point
(1) Tangent at a point
A tangent of a circle is perpendicular to the radius of the circle drawn from the point of contact.
(2) Tangent from an external point
It there are two tangents from an external point to a circle,
-the length of the tangents are equal
-the line joining the external point and the centre bisects the angle between the tangents
Angle properties of circles
Arc and segments of a circle
<(in our notes given by Mrs. Sim, on pg 1, we highlighted the arc to show big and small arch plus shade to show the segments, it look something like the one I drew.)>
- Angles in a circle
(1) Angle at centre = 2 × angle at circumference subtended by an arc (angle at centre = 2 x angle at circumference)
(2) An angle in the semicircle is a right angle (angle in a semicircle)
(3) Angles in the same segment are equal (angles in the same segment)
- Angles in the opposite segments (angles in opp. segments)
Here we will display questions for you to try out on your own. GD LUCK(:
SOURCE:www.google.com
In the diagram, the points A, B, C, D and E lie on the circumference of the two circles such that AEDC forms a cyclic quadrilateral and BCD is a straight line. The centre of the smaller circle is marked as O. Given that AB = BC, AE = CE, angle AED = 65° and angle ACE = 70°, find
In the diagram, AB is the diameter of the circle with centre O. CE and BE are tangents to the circle. The tangent to the circle at point B meets OC produced at D. Given that angle CBE = 28° and that the radius of the circle is 5cm, find,
(i) angle BEC
(ii) angle CAO
(iii) length of BC
(iv) angle CDE
ANSWERS:
(i) angle ACB = angle AED = 65° (ext. angle of cyclic quad.)
(ii) angle ABC = 180° - 2 x 65° (sum of triangle)
= 50°
(iii) angle AOC = 50° x 2 (angle at centre= 2 angle at circumference)
= 100°
angle OAC = (180° - 100°)
= 40°
(iv) angle AEC = 180° - 2 x 70°
= 40°
angle ADC = 40° ( angles in the same segment)
(i) BEC is an isos. triangle
angle BEC = 180° - 2 x 28°
= 124°
(ii) angle CAD = angle CBE = 28° (alt. segment theorem)
(iii) triangle ACB is a rt. triangle and AB = 10cm
sin 28° = BC/10
BC = 10 sin 28°
= 4.69 cm (3s.f.)
(iv) angle COB = 28° x 2 (angle at centre= 2 angle at circumference)
= 56°
angle OBD = 90°
angle CDE = 180° - 56° - 90°
= 34°
There is a time for everything, this time, its the time to share.
Chats
REFLECTIONS of members:
Keith:
I feel that this project is really useful as it helps us gain a deeper understanding into the “properties of circles” topic. Having gained this knowledge I think that I will be better at answering mathematical questions concerning this topic. This project also helps to improve the teamwork, communication and understanding between us, as teammates, in order to complete the project smoothly, we need to learn to cooperate with our classmates.
Shu Yi:In my opinion, the properties of the circles is just basically an aid to help us to find the angles in the circle. There are many different types of properties for us to memorise in order for us to find the angles in the circle easily and in the shortest amount of time. Some of the properties of circles include:
-Perpendicular from centre bisects chord.
-Equal chords, equidistant from centre.
-Angle at centre is equals to two times the angle at the circumference.
-Angle in a semicircle.
-Angles in the same segment.
-Angles in the opposite segments.
-Tangent bisects radius.
-Tangent from an external point.
There are so many properties such that it can drive us crazy! But as long as we can memorise them and use them at the right time, this topic isn’t hard to learn at all.
There are also many other points and factors that are very important and are related to the properties as mentioned above.
Circumference- It is basically the sides of the circle, meaning the line segment.
Tangent- A tangent is which is in such a way that it is perpendicular to the centre of the circle when a line is drawn from it.
Chord- A chord is basically a line segment where the two ends of it touches the circumference of the circle.
These points are the basics before we can learn the properties of the circles. Basically, in my eyes, the properties of the circles don’t seem to be the properties of it, but the properties of the angles in it. All the methods used to find the properties of the circles are meant to find the angles in the circle compound.
Arffah:
I feel that through this project I can have a better understanding of the properties of circles and in the same time have fun designing and making our blog attractive. I was also able to learn about moral values such as the importance of having teamwork whereby each member fulfils his/her role and contributes to the work. I also realized that it is important to hear out everyone’s opinion on a matter and decide on the best solution to ensure the project is a success. Learning seems so much easier and I feel that I am able to digest what I put up on the blog more easily.
Tian Cong:
Through this project, I managed to have a much better understanding of the properties of circles. Having this project not only let me have a better understanding of this topic, but also allows me to share this knowledge i have with the rest of my friends. Doing this project in blog way allow us to have fun, because we get to design our blog the way we want. On the other hand, doing project in the form of blog is much more efficient as it allow us as students to save some meeting time, especially we only have a short period to complete this project. I learn that it is very important for each member to complete their assigned task well and on time, so that the leader would have a much easier time adding up all the works from the group members. Hopefully, we get to do our projects in the form of a blog or webpage form more often in the future.
Afiqah:
this project give us a better understanding on the properties of angles and how to solve the circles problems because we have to personally do a research about it. Like others, we did not gain in terms of practice of moral values but also extra knowledge that we gotten from the research. We are glad to be given the opportunities to share our knowledge.
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