Properties of Circles
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Teaching Concept Two
- The chord of a circle that passes through the centre of the circle is called the Perepndicular Bisector.
- Therefore, in equal circles or in the same circle, equal chords are equidistant from the centre.
- In another words, chords which are equidistant from the centre are equal.
- With this property, we are able to locate the centre of the circle.
Proof:
- In the figure below, triangle OAB is rotated through an angle AOA' to triangle OA'B' about O.
- Since rotation preserves the shape and size, AB = A'B' and OG = OH. [Proven]
- Let us try a Simple Question.
If you are a designer for the construction of the Ferry Wheel in Genting Highland, using this property which you have just learnt, explain how would you find the centre of the Flyer?
~ Math Teaching Blog ~
In this Blog.. You will learn about the 4 Properties of Circles.
~ Chords of a Circle ~The Perpendicular bisector of a Chord of a Circle passes through the Centre of the Circle
Equal Chords of a Circle are Equildistant from the Centre of the Centre
The Perpendicular from the centre of a Circle to a Chord bisects the Chord
~ Angles in a Circle ~The angle subtended by an arc at the centre of a Circle is twice the angle subtended by the same arc at the Circumference
An angle in a Semicircle is a Right- angle
The angles in the same segment of a Circle are equal
~ Angles in the Opposite Segments ~The sum of the angles in the Opposite Segments of a Circle is 180 degree
~ Tangents to a Circle ~A tangent of a Circle is perepndicular to the Radius of the Circle drawn from the point of Contact
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