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Question

In the given figure, radius of the circle is 5 cm and perpendicular distance from the centre of the circle to the chord, AC is 3 cm.

Find the length of the chord, AC.


A

4 cm

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B

5 cm

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C

7 cm

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D

8 cm

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Solution

The correct option is D

8 cm


In OAB, applying Pythagoras Theorem:

OA2=OB2+AB2

52=32+AB2

AB2=5232=259=16

AB=16=4 cm

We know that perpendicular from the centre of the circle to the chord, bisects the chord.

AB=BC

Now, AC=AB+BC

AC=AB+AB=2AB [AB=BC]

AC=2×4=8 cm


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