RPF Constable practice question
Two circles intersect such that the distance between their centres is 8 cm and the length of their common chord is 42 cm. If the radius of one circle is 35 cm, find the radius of the other circle.
From a RPF Constable Quantitative Aptitude practice set · Quantitative Aptitude
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Correct answer: (A) 29 cm
Half the chord h = 42/2 = 21 cm. For the circle of radius 35 cm, the foot of perpendicular M from its centre O1 satisfies O1M = √(35² − 21²) = 28 cm. Since O1O2 = 8 cm, O2M = |8 − 28| = 20 cm. So the required radius = √(O2M² + h²) = √(20² + 21²) = 29 cm.
हिंदी में प्रश्न
दो वृत्त इस प्रकार प्रतिच्छेद करते हैं कि उनके केंद्रों के बीच की दूरी 8 सेमी है और उभयनिष्ठ जीवा की लंबाई 42 सेमी है। यदि एक वृत्त की त्रिज्या 35 सेमी है, तो दूसरे वृत्त की त्रिज्या ज्ञात कीजिए।
उत्तर जाँचने के लिए किसी विकल्प पर टैप करें।
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सही उत्तर: (A) 29 सेमी
आधी जीवा h = 42/2 = 21 सेमी है। 35 सेमी त्रिज्या वाले वृत्त के लिए, उसके केंद्र O1 से लंब का पाद M इस प्रकार है कि O1M = √(35² − 21²) = 28 सेमी। चूँकि O1O2 = 8 सेमी, O2M = |8 − 28| = 20 सेमी। अतः अभीष्ट त्रिज्या = √(O2M² + h²) = 29 सेमी।
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