Tangents

• Concept of tangent at any point of the circle

 

Theorem: The tangent at any point on a circle is perpendicular to the radius through the point of contact.

 

Example: 

A tangent AB at a point A of a circle of radius 6 cm meets a line through the centre O at the point B, such that OB = 10 cm. Find the length of AB.

Solution:

 

It is known that the tangent at any point on a circle is perpendicular to the radius through the point of contact.
OA ⊥ AB
 

By applying Pythagoras theorem in right triangle OAB, we obtain

OA² + AB² = OB²
⇒ 6² + AB² = 10²
⇒ AB² = (100 − 36) cm²
⇒ AB² = 64 cm²
$\Rightarrow \mathrm{AB}=\sqrt{64 {\mathrm{cm}}^2}=8 \mathrm{cm}$

No tangent can be drawn to a circle passing through a point lying inside the circle.

One and only one tangent can be drawn t…