Question:
In a circle with center \(O\), a \(6\) cm long chord is at a distance \(4\) cm from the center. Then the length of diameter is
In a circle with center \(O\), a \(6\) cm long chord is at a distance \(4\) cm from the center. Then the length of diameter is
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The perpendicular from the center to a chord bisects the chord.
Updated On: May 7, 2026
- \(5\) cm
- \(10\) cm
- \(15\) cm
- \(8\) cm
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The Correct Option is B
Solution and Explanation
Step 1: Chord length is \(6\) cm, so half chord is: \[ \frac{6}{2}=3\text{ cm} \]
Step 2: Distance from center to chord is: \[ 4\text{ cm} \]
Step 3: Radius, half chord, and perpendicular distance form a right triangle. \[ r^2=3^2+4^2 \] \[ r^2=9+16=25 \] \[ r=5\text{ cm} \]
Step 4: Diameter is: \[ 2r=2(5)=10\text{ cm} \] \[ \boxed{10\text{ cm}} \]
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