Question : In a circle, the length of a chord is 30 cm. The perpendicular distance of the chord from the centre of the circle is 8 cm. Find the diameter of the circle.
Option 1: 28 cm
Option 2: 34 cm
Option 3: 17 cm
Option 4: 30 cm
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Correct Answer: 34 cm
Solution :
Let AB be the chord and O be the center of the circle.
Also, OP is perpendicular to AB
In $\triangle$ OPB,
OB
2
= PB
2
+ OP
2
⇒ OB
2
= 15
2
+ 8
2
⇒ OB
2
= 225 + 64
⇒ OB
2
= 289
⇒ OB = $\sqrt{289}$
⇒ OB = 17 cm
Diameter = 2 × OB = 2 × 17 = 34 cm
∴ The diameter of the circle is 34 cm.
Hence, the correct answer is 34 cm.
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