Question
Download Solution PDF10 सेमी त्रिज्या असलेल्या एका वर्तुळाच्या केंद्रापासून 8 सेमी अंतरावर असलेल्या जीवेची लांबी शोधा.
Answer (Detailed Solution Below)
Detailed Solution
Download Solution PDFदिलेल्या प्रश्नानुसार,
दिलेले आहे:
वर्तुळाची त्रिज्या = 10 सेमी
केंद्रापासूनचे अंतर = 8 सेमी
वापरलेले सूत्र:
वर्तुळाचे केंद्र व त्या वर्तुळातील जीवेचा मध्यबिंदू जोडणारा रेषाखंड हा त्या जीवेला लंब असतो.
पायथागोरसच्या प्रमेयानुसार, एका काटकोन त्रिकोणाच्या कर्णाच्या लांबीचा वर्ग हा इतर दोन बाजूंच्या वर्गाच्या बेरजेइतका असतो.
गणना:
समजा, जीवेची लांबी = AB
त्रिकोण AOC मध्ये, पायथागोरस प्रमेयानुसार,
∴ (10)2 = (8)2 + AC2
⇒ AC2 = (10)2 - (8)2
⇒ AC = 6
आता, जीवा AB ची लांबी = AC + (BC व OC हे जीवेला दोन समान भागात विभागतात)
∴ AB = AC + BC = 2 × AC = 2 × 6 = 12 सेमी
म्हणून, जीवेची लांबी = 12 सेमी
म्हणून, पर्याय (2) योग्य आहे.
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