6.3.1 Tangents to a Circle
1. A tangent to a circle is a straight line that touches the circle at only one point and the point is called the point of contact.
![](http://spmmathematics.blog.onlinetuition.com.my/wp-content/uploads/sites/5/2015/01/Picture6.png)
![](http://spmmathematics.blog.onlinetuition.com.my/wp-content/uploads/sites/5/2015/01/Picture6.png)
2. If a straight line cuts a circle at two distinct points, it is called a secant. The chord is part of the secant in a circle.
![](http://spmmathematics.blog.onlinetuition.com.my/wp-content/uploads/sites/5/2015/01/Picture4.png)
![](http://spmmathematics.blog.onlinetuition.com.my/wp-content/uploads/sites/5/2015/01/Picture4.png)
3. Tangent to a circle is perpendicular to the radius of the circle that passes through the point of contact.
![](http://spmmathematics.blog.onlinetuition.com.my/wp-content/uploads/sites/5/2015/01/Picture5.png)
If ABC is the tangent to the circle at B, then
ABO =
CBO = 90o.
Properties of Two Tangents to a Circle from an External Point
![](http://spmmathematics.blog.onlinetuition.com.my/wp-content/uploads/sites/5/2015/01/Picture8.png)
In the diagram, BA and BC are two tangents from an external point B. The properties of the tangents are as follows.
(a) BA = BC
(b)
ABO =
CBO = xo
(c)
AOB =
COB = yo
(d) ∠ OAB =
OCB = 90o
(e)
AOC +
ABC = 180o
(f) ∆ AOB and ∆ COB are congruent
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