जब त्रिज्या r1 और r2 के दो वृत्तों के केंद्र d दूरी पर हों, तो तिर्यक उभयनिष्ठ अनुप्रस्थ स्पर्श रेखा की लंबाई क्या होगी? 

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SSC CGL 2023 Tier-I Official Paper (Held On: 25 Jul 2023 Shift 1)
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  1. \(\sqrt{d^2 - (r_1 - r_2)^2}\)
  2. \(\sqrt{d^2 + (r_1 - r_2)^2}\)
  3. \(\sqrt{d - (r_1 - r_2)^2}\)
  4. \(\sqrt{d^2 - (r_1 + r_2)^2}\)

Answer (Detailed Solution Below)

Option 4 : \(\sqrt{d^2 - (r_1 + r_2)^2}\)
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दिया गया​ है:

प्रथम वृत्त की त्रिज्या = r1

दूसरे वृत्त की त्रिज्या = r2

वृत्त के केंद्र के बीच की दूरी = d

गणना:

तिर्यक उभयनिष्ठ अनुप्रस्थ स्पर्श रेखा की लंबाई = \(\sqrt{d^2 - (r_1 + r_2)^2}\)

∴ सही विकल्प 4 है। 

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