Given a circle with centre O and OB is perpendicular to the chord AM. If the length of AM is 8 cm, then find the length of AB.

5 cm

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4 cm

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6 cm

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2 cm

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Solution

The correct option is B 4 cm
The perpendicular from the centre of a circle to the chord will always bisect the chord (split it into two equal lengths).

i.e, OB will divide the chord AM into two equal halves
$\Rightarrow A B = B M = \frac{1}{2} A M$
$\Rightarrow A B = \frac{1}{2} \times 8 = 4 c m$

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