F2 Savita SSC 21-8-24 D4

वरील आकृतीत दाखवल्याप्रमाणे दोन वर्तुळे एकमेकांना बाहेरून स्पर्श करतात. O केंद्र असलेल्या वर्तुळाची त्रिज्या 49 सेमी आहे. केंद्र A असलेल्या वर्तुळाची त्रिज्या 16 सेमी आहे. त्यांच्या सामान्य स्पर्शिका BC ची लांबी (सेमी मध्ये) शोधा.

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SSC CHSL Exam 2024 Tier-I Official Paper (Held On: 02 Jul, 2024 Shift 1)
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  1. 55
  2. 58
  3. 57
  4. 56

Answer (Detailed Solution Below)

Option 4 : 56
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दिले:

केंद्र O (r1) असलेल्या वर्तुळाची त्रिज्या = 49 सेमी.

A (r2) केंद्र असलेल्या वर्तुळाची त्रिज्या = 16 सेमी.

वापरलेले सूत्र:

सामान्य स्पर्शिकेची लांबी = \(\sqrt{d^2-(r_1 -r_2)^2}\)

जिथे, d = केंद्रातील अंतर

गणना:

केंद्रातील अंतर = 49 + 16 = 65

तर,

सामान्य स्पर्शिकेची लांबी

\(\sqrt{65^2-(49 -16)^2} \)

\(\sqrt{65^2-33^2} \)

\(\sqrt{(65+33)(65-33)}\)

\(\sqrt{98× 32} \)

\(\sqrt{98× 2×16} \)

⇒ 7 × 2 × 4 = 56 सेमी

∴ योग्य उत्तर पर्याय (4) आहे.

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