Question

A tangent AB at a point A of a circle of radius
5 cm meets a
line through the centre at O at a
point B so that
OB = 13 cm. find length of AB.

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Answer 1

Step-by-step explanation:

In figure, AB is the tangent of circle (O,r).

Here r = 5 cm. = AO and OB = 12 cm.

Since tangent is perpendicular to radius OA, therefore OAB is a right triangle.

Now in rt Δ OAB, ∠A=90

∘

Thus OB

2

=OA

2

+AB

2

⇒12

2

=5

2

+AB

2

⇒AB

2

=144−25=119

Therefore, AB=

119

cm

solution