Question
Download Solution PDFत्रिभुज ABC में, AB = 12 सेमी, BC = 16 सेमी और AC = 20 सेमी है। त्रिभुज के अंदर एक वृत्त अंकित है। वृत्त की त्रिज्या (सेमी में) क्या है?
Answer (Detailed Solution Below)
Detailed Solution
Download Solution PDFदिया गया है:
त्रिभुज ABC में, AB = 12 सेमी, BC = 16 सेमी, AC = 20 सेमी
प्रयुक्त सूत्र:
त्रिभुज का क्षेत्रफल (Δ) = \(\sqrt{s(s-a)(s-b)(s-c)}\)
जहाँ s = अर्ध-परिमाप = \(\frac{a+b+c}{2}\)
अंकित वृत्त की त्रिज्या (r) = \(\frac{\Delta}{s}\)
गणनाएँ:
a = 12 सेमी, b = 16 सेमी, c = 20 सेमी
s = \(\frac{12+16+20}{2}\) = 24 सेमी
क्षेत्रफल (Δ) = \(\sqrt{24(24-12)(24-16)(24-20)}\)
⇒ क्षेत्रफल (Δ) = \(\sqrt{24×12×8×4}\)
⇒ क्षेत्रफल (Δ) = \(\sqrt{9216}\)
⇒ क्षेत्रफल (Δ) = 96 सेमी2
त्रिज्या (r) = \(\frac{96}{24}\)
⇒ त्रिज्या (r) = 4 सेमी
∴ सही उत्तर विकल्प (2) है।
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