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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