Question
Download Solution PDFएक समद्विबाहु ΔMNP एक वृत्त में उत्कीर्ण है। यदि MN = MP = \(16\sqrt{5}\) सेमी, और NP = 32 सेमी, वृत्त की त्रिज्या (सेमी में) कितनी है?
Answer (Detailed Solution Below)
Detailed Solution
Download Solution PDFदिया गया है:
MN = MP = 16√5 सेमी
NP = 32 सेमी
प्रयुक्त सूत्र:
त्रिभुज का क्षेत्रफल = (1/2) × आधार × ऊँचाई
परित्रिज्या = ABC/4Δ
जहाँ A, B और C त्रिभुज की तीन भुजाएँ हैं
Δ = त्रिभुज का क्षेत्रफल
गणना:
MD, NP पर लम्ब है
तो, ND = DP = 32/2 = 16 सेमी
MD = √[(16√5)2 - (16)2] = √(1280 - 256) = √1024 = 32 सेमी
ΔMNP का क्षेत्रफल = (1/2) × 32 × 32 = 512 वर्गसेमी
परित्रिज्या = (16√5 × 16√5 × 32)/(4 × 512) = 20 सेमी
∴ वृत्त की त्रिज्या (सेमी में) 20 सेमी है
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