- 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.
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.
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
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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