Question : In a circle of radius 8 units, a chord of length 10 units is drawn. What is the perpendicular distance of the chord from the centre of the circle in units?
Option 1: $\sqrt{39}$ Units
Option 2: $\sqrt{35}$ Units
Option 3: $\sqrt{30}$ Units
Option 4: $\sqrt{33}$ Units
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Correct Answer: $\sqrt{39}$ Units
Solution : Let O be the centre of the circle of radius 8 units. Let AB be the chord of length 10 units. Let OD be perpendicular from the centre to the chord AB. We know the perpendicular from the centre to a chord bisects the chord. So, AD = BD = 5 units Applying Pythagoras theorem in $\triangle$OBD, OB2 = OD2 + DB2 ⇒ 82 = OD2 + 52 ⇒ OD2 = 64 – 25 $\therefore$ OD = $\sqrt{39}$ units Hence, the correct answer is $\sqrt{39}$ units.
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Question : A chord is drawn in a circle of radius 10 cm, if the distance of the chord from the centre is 6 cm, then the length of the chord (in cm) is:
Option 1: 10
Option 2: 12
Option 3: 16
Option 4: 8
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
Question : Half of the length of a chord of a circle is 12 cm and the perpendicular distance between the centre and the chord is 5 cm. The radius of the circle is:
Option 1: 12 cm
Option 2: 13 cm
Option 3: 10 cm
Option 4: 24 cm
Question : The perpendicular distance from the centre of a circle to the chord is 20 cm. Calculate the chord's length in centimetres if the circle's diameter is 58 cm.
Option 1: 42
Option 2: 21
Option 3: 56
Option 4: 28
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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