Two parallel chords on the same side of the centre of a circle are 12 cm and 20 cm long and the radius of the circle is $5 \sqrt{13}$ cm. What is the distance between the chords?
Two parallel chords on the same side of the centre of a circle are 12 cm and 20 cm long and the radius of the circle is $5 \sqrt{13}$ cm. What is the distance between the chords?
एक वृत्त के केंद्र के एक ही और 12 cm और 20 cm लंबाई की दो समान्तर जीवाएँ हैं और वृत्त की त्रिज्या$5 \sqrt{13}$ cm हैं। इन जीवाओं के बीच की दूरी कितनी होगी?
Detailed Solution & Logic
Correct Answer:
2 cm
Simple solution / सरल हल:
Radius r=513r = 5\sqrt{13}r=513
Distance of a chord from centre:
$d = \sqrt{r^2 - \left(\frac{L}{2}\right)^2}$
For 12 cm chord:
$d_1 = \sqrt{325 - 36} = \sqrt{289} = 17$ cm
For 20 cm chord:
$d_2 = \sqrt{325 - 100} = \sqrt{225} = 15$ cm
Distance between chords = $17 - 15 = 2$ cm
Final Answer: 2 cm
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