Question : The distance of a chord JK from the centre is 7 cm. If the diameter of this circle is 50 cm, then what will be the length of this chord?
Option 1: 74 cm
Option 2: 96 cm
Option 3: 48 cm
Option 4: 24 cm
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Correct Answer: 48 cm
Solution :
The radius of the circle is half the diameter.
The radius = $\frac{50}{2}$ = 25 cm
Let the length of the chord JK = $2x$ cm
The distance from the centre of the circle to the chord = 7 cm
The perpendicular from the centre of a circle to a chord bisects the chord,
So, JP = $x$ cm
Applying the pythagorean theorem, we get:
$⇒x = \sqrt{r^2 - d^2} = \sqrt{25^2 - 7^2} = \sqrt{576} = 24$
The length of the chord (in cm) JK $= 2x = 2 \times 24 = 48\ \text{cm}$
Hence, the correct answer is 48 cm.
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