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

OA^{2} + AB^{2} = OB^{2}

⇒ 6^{2} + AB^{2} = 10^{2}

⇒ AB^{2}^{ }= (100 − 36) cm^{2}

⇒ AB^{2} = 64 cm^{2}

$\Rightarrow \mathrm{AB}=\sqrt{64{\mathrm{cm}}^{2}}=8\mathrm{cm}$

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…

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