Question : The radius of a circle is 5 cm. The length of chord AB in this circle is 6 cm. What is the distance of this chord from the centre of the circle?
Option 1: 4 cm
Option 2: 5 cm
Option 3: 6 cm
Option 4: 8 cm
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Correct Answer: 4 cm
Solution : Let $OB$ be the radius of the circle and $OD$ be the distance from the centre to the chord $AB$. The radius of a circle, $OB$ = 5 cm Length of chord $AB$ = 6 cm Now, we know altitude from the centre of a circle to its chord bisects the chord. So, $BD$ = 3 cm Applying Pythagoras theorem, we get: $OB^2=BD^2+OD^2$ ⇒ $5^2=3^2+OD^2$ $\therefore OD=4$ cm Hence, the correct answer is 4 cm.
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