Question : In a circle with a centre at O(0,0) and a radius of 5 cm, AB is a chord of length 8 cm. If OM is perpendicular to AB, then the length of OM is:
Option 1: 2.5 cm
Option 2: 3 cm
Option 3: 4 cm
Option 4: 1 cm
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Correct Answer: 3 cm
Solution :
Given , AB = 8 cm
We know that the perpendicular from the centre of a circle to a chord bisects the chord.
AM = MB = $\frac{1}{2}×8=4$ cm
OA = 5 cm
From ∆ AOM,
OA
2
= OM
2
+ AM
2
⇒ OM $=\sqrt{5^2-4^2}=3$ cm
Hence, the correct answer is 3 cm.
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