Question
Download Solution PDFखालील 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.
Answer (Detailed Solution Below)
Detailed Solution
Download Solution PDFदिलेल्याप्रमाणे:
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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