A line through the centre O of a circle of radius 20 cm cuts the tangent drawn from a point A on the circle, at point B such that AB = 21 cm. The length of OB is

30 cm

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29 cm

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32 cm

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34 cm

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Solution

The correct option is B
29 cm
Given AB = 21 cm

Here, $O A ⊥ A B$
$(∵ Angle between a tangent and radius of circle is 90^{\circ}) I n Δ O A B, A p p l y P y t h a g o r a s t h e o r e m O B^{2} = O A^{2} + A B^{2} = 20^{2} + 21^{2} = 400 + 441 = 841 \Rightarrow O B = \sqrt{841} \Rightarrow O B = 29 c m$
Hence, the correct answer is option b.

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A line through the centre O of a circle of radius 20 cm cuts the tangent drawn from a point A on the circle, at point B such that AB = 21 cm. The length of OB is

The correct option is B 29 cmGiven AB = 21 cm Here, OA⊥ AB (∵Angle between a tangent and radius of circle is 90∘)In Δ OAB,Apply Pythagoras theoremOB2=OA2+AB2=202+212=400+441=841⇒OB=√841⇒OB=29 cm Hence, the correct answer is option b.