Question : The length of the chord of a circle is 8 cm and the perpendicular distance between the centre and the chord is 3 cm, then the diameter of the circle is equal to:
Option 1: 5 cm
Option 2: 10 cm
Option 3: 3 cm
Option 4: 7 cm
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Correct Answer: 10 cm
Solution :
Distance of perpendicular from centre to chord, $OD=3$ cm
Length of chord, $AB=8$ cm
We know that perpendicular from the centre to the chord bisects the chord.
So, $AD=BD = 4$ cm
Radius = $OB$
In $\Delta OBD$
$OB^2=BD^2+OD^2$
⇒ $OB^2=4^2+3^2$
⇒ $OB=5$ cm
⇒ Diameter, $AB = 2OB = 10$ cm
Hence, the correct answer is 10 cm.
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