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.
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.
3. Tangent to a circle is perpendicular to the radius of the circle that passes through the point of contact.
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
In the diagram, BA and BC are two tangents from an external point B. The properties of the tangents are as follows.
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(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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