Question
Download Solution PDFएक समबाहु त्रिभुज का एक शीर्ष (-1, -1) पर है और दूसरा शीर्ष \(\left( { - \sqrt 3 ,\;\sqrt 3 } \right)\) पर है। तीसरा शीर्ष कहाँ पर हो सकता है?
Answer (Detailed Solution Below)
Detailed Solution
Download Solution PDFधारणा:
एक समबाहु त्रिभुज की सभी भुजाएँ समान होती हैं।
गणना:
माना कि,
A = (-1, -1),
B = \(\left( -\sqrt{3},~\sqrt{3} \right)\) और
C = (x, y)
∵ वे एक समबाहु त्रिभुज के शीर्ष हैं ⇒ AB = BC = AC
\(A{{B}^{2}}={{\left( -\sqrt{3}+1 \right)}^{2}}+{{\left( \sqrt{3}+1 \right)}^{2}}=8~units\)
उसीप्रकार,
\(B{{C}^{2}}={{\left( x+\sqrt{3} \right)}^{2}}+{{\left( y-\sqrt{3} \right)}^{2}}={{x}^{2}}+{{y}^{2}}+2\sqrt{3}~\left( x-y \right)+6=8\) ----(1)
\(A{{C}^{2}}={{\left( x+1 \right)}^{2}}+{{\left( y+1 \right)}^{2}}={{x}^{2}}+{{y}^{2}}+2\left( x+y \right)+2=8\) ----(2)
(1) और (2) से हम प्राप्त करते हैं
\(\Rightarrow ~2\sqrt{3}~\left( x-y \right)+6=~2\left( x+y \right)+2\)
⇒ x = y = 1Last updated on Jul 8, 2025
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