6.3.1 Tangents to a Circle - Mathematics

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 = 90^o.

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.

(a) BA = BC

(b)

∠

$∠$ ABO =

∠

$∠$ CBO = x^o

(c)

∠

$∠$ AOB =

∠

$∠$ COB = y^o

(d) ∠ OAB =

∠

$∠$ OCB = 90^o

(e)

∠

$∠$ AOC +

∠

$∠$ ABC = 180^o

(f) ∆ AOB and ∆ COB are congruent