Question
Download Solution PDFत्रिज्या 10 सेमी असलेल्या वर्तुळाचा जीवा AB केंद्र O पासून 8 सेमी अंतरावर आहे. जर A आणि B वर काढलेले स्पर्शक P वर छेदतात, तर स्पर्शिका AP ची लांबी (सेमी मध्ये) किती आहे?
Answer (Detailed Solution Below)
Detailed Solution
Download Solution PDFदिलेले आहे:
त्रिज्या = 10 सेमी
वापरलेली संकल्पना:
सादृश्याची संकल्पना
AAA सादृश्य → जर एका त्रिकोणातील सर्व तीन कोन दुसऱ्या त्रिकोणातील संबंधित कोनांसारखे असतील, तर ते त्रिकोण सादृश्य असतात.
गणना:
दिलेल्या आकृतीत,
ΔDAO ∼ ΔAPO [∵ ∠OAP = ∠ODA = 90° आणि ∠AOD दोन्ही त्रिकोणांमध्ये समान आहे]
म्हणून,
AD/AP = DO/AO
⇒ 6/AP = 8/10 [6, 8, 10 पायथागोरस त्रिकूट]
⇒ AP = 60/8
⇒ AP = 7.5 सेमी
∴ स्पर्शिका AP ची लांबी 7.5 सेमी आहे
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