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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Question : The radius of a circle is 10 cm. The distance of chord PQ from the centre is 8 cm. What is the length of chord PQ?
Option 1: 16 cm
Option 2: 15 cm
Option 3: 12 cm
Option 4: 14 cm
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
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 : A chord of length 24 cm is at a distance of 5 cm from the centre of the circle. The radius of the circle is:
Option 1: 13 cm
Option 2: 12 cm
Option 3: 16 cm
Option 4: 15 cm
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