Question : The radius of a circle is 5 cm and the length of one of its chords is 8 cm. Find the distance of the chord from the centre.
Option 1: 3 cm
Option 2: 4 cm
Option 3: 5 cm
Option 4: 2 cm
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Correct Answer: 3 cm
Solution : Radius of circle with centre $O$ is $OB$ = $5$ cm Length of chord $AB = 8$ cm We know that perpendicular from the centre to the chord bisects the chord. So, $OD \perp AB$ which bisects $AB$ at $D$. ∴ $AD=DB=4$ cm In $\Delta OBD$, $OB^2=OD^2+BD^2$ (Pythagoras theorem) ⇒ $(5)^2=OD^2+(4)^2$ ⇒ $OD=3$ Hence, the correct answer is 3 cm.
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