Math Teaching on Properties of Circles

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Properties of Circles

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Monday, July 20, 2009

Teaching Concept Three

Let us look at the 2nd Symmetrical Property of Circles:
- 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]

# posted by Properties of Circles at 3:25:00 AM