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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