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A tangent to a circle is a straight line that touches a circle
at one point only.
For example, PT is a tangent to the following circle at the
point P. We call P the point of contact.
Note:
A tangent is perpendicular to the radius at the point of contact.
Example 20
If PA and PB are two tangents to a circle centred at O,
prove that:
a. PA = PB
b. u = v
c. x = y
Proof:
In general:
If PA and PB are two tangents to a circle centred at O,
then:
- the tangents to the circle from the external point P are
equal
- OP
bisects the angle between the two tangents
- OP
bisects the angle between the two radii to the points of
contact
Example 21
Find the value of the pronumeral(s) in each of the following diagrams: |
