Properties of Circles
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Teaching Concept Three
- SInce a circle is symmetrical about every diameter.
- Therefore any chord AB that is perpendicular to a diameter is bisected by the diameter.
- Also, any chord bisected by a diameter is perpendicular to the diameter.
- How to proof if the chord is always bisected to the diameter?
Proof:
- In a given a circle, centre O and chord AB, with a mid- point D, we are required to show that OĈB= 90°.
- 1st, you join OA and OB together.
- You can see that in triangle OAC and OBC,
OA= OB [radii of circle]
AC= BC [given]
OC is common.
- Triangle OCD is congruent to triangle OBC [SSS property].
OĈA = OĈB.
- Since these are adjacent angles on a straight line, therefore you can say that OĈA= OĈB= 90°. [proven]
~ 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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