Question
Download Solution PDFएक समद्विभुज ΔMNP वर्तुळात कोरलेला आहे. जर MN = MP = \(16\sqrt{5}\) सेमी, आणि NP = 32 सेमी, वर्तुळाची त्रिज्या (सेमी मध्ये) किती आहे?
Answer (Detailed Solution Below)
Detailed Solution
Download Solution PDFदिलेले आहे:
MN = MP = 16√5 सेमी
NP = 32 सेमी
वापरलेले सूत्र:
त्रिकोणाचे क्षेत्रफळ = (1/2) × पाया × उंची
परित्रिज्या = ABC/4Δ
जिथे. A, B आणि C या त्रिकोणाच्या तीन बाजू आहेत
Δ = त्रिकोणाचे क्षेत्रफळ
गणना:
MD हा NP ला लंब आहे
म्हणून, ND = DP = 32/2 = 16 सेमी
MD = √[(16√5)2 - (16)2] = √(1280 - 256) = √1024 = 32 सेमी
ΔMNP चे क्षेत्रफळ = (1/2) × 32 × 32 = 512 सेमी2
परित्रिज्या = (16√5 × 16√5 × 32)/(4 × 512) = 20 सेमी
∴ वर्तुळाची त्रिज्या 20 सेमी आहे.
Last updated on Jun 13, 2025
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