Math Teaching on Properties of Circles

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Properties of Circles

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Tuesday, July 21, 2009

Teaching Concept Nine

Let us take a look at the 1st Property of Tangents to a Circle:
- A tangent of a circle is perpendicular to the radius of the circle drawn from the point of contact.

- In the figure on the right, P is a point outside the circle, with centre O, line PA and line PB are two tangents drawn from P to touch the circle at A and B respectively.
- We can find that
i) line AP= line BP
ii) angle APO= angle BPO
iii) angle AOP= angle BOP

- Since, angle OAP= angle OBP= 90° (tangent perpendicular radius)
and △ AOP and △ BOP are congruent (R. H. S Property)
- Therefore, line AP= line BP,
angle APO= angle BPO,
and angle AOP= angle BOP

- We can also conclude that:
i) tangents drawn to a circle from an external point are equal.
ii) the tangents subtend equal angles at the centre.
iii) the line joining the external point to the centre of the circle bisects the angle between the tangents.

# posted by Properties of Circles at 3:08:00 AM