Question : The perpendicular distance from the centre of a circle to the chord is 20 cm. Calculate the chord's length in centimetres if the circle's diameter is 58 cm.
Option 1: 42
Option 2: 21
Option 3: 56
Option 4: 28
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Correct Answer: 42
Solution :
Given:
Diameter, AB = $58$ cm
So, Radius = $\frac{58}{2}=29$ cm
CD is the chord.
Its distance from the centre, ON is $20$ cm.
CD = $2$ × CN
Join OC.
OC is the radius.
From $\triangle$OCN,
OC
2
= ON
2
+ CN
2
⇒ $29^2=20^2$+CN
2
⇒ CN
2
= $841-400$
⇒ CN = $21$ cm
So, CD = $2 × 21 = 42$ cm
So, the length of the chord is 42 cm.
Hence, the correct answer is 42.
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