खालील आकृतीत, केंद्र B आणि D असलेल्या वर्तुळांच्या त्रिज्या अनुक्रमे 4 सेमी आणि x सेमी आहेत. AC ही दोन्ही वर्तुळांची स्पर्शिका आहे. x चे मूल्य काढा.

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SSC CGL 2023 Tier-I Official Paper (Held On: 25 Jul 2023 Shift 4)
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  1. 6
  2. 3
  3. 7
  4. 5

Answer (Detailed Solution Below)

Option 1 : 6
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PYST 1: SSC CGL - General Awareness (Held On : 20 April 2022 Shift 2)
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दिलेल्याप्रमाणे:

लहान वर्तुळाची त्रिज्या (r) = 4 सेमी

AE = 6 सेमी; EC = 9 सेमी

वापरलेली संकल्पना:

स्पर्शबिंदूवर स्पर्शिका वर्तुळाच्या त्रिज्येसोबत काटकोन तयार करते.

अनुलंब विरुद्ध कोन समान आहे.

गणना:

AD ⊥ AC आणि BC ⊥ AC

∠DAE = ∠BCE = 90°

△DAE आणि △BCE मध्ये

∠DAE = ∠BCE = 90°

∠AED = ∠BEC (अनुलंब कोन)

△DAE ~ △BCE (AA समरूपतेने)

C.P.C.T द्वारे

⇒ AE/EC = AD/BC

⇒ 6/9 = 4/BC

⇒ BC = 36/6 = 6 सेमी

म्हणूनच योग्य उत्तर 6 सेमी आहे.

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