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Asked by Vedikapatil3104 | 05 Sep, 2019, 20:31: PM
answered-by-expert Expert Answer
L e t space A left parenthesis 0 comma 0 right parenthesis comma space B space l i e s space o n space t h e space l i n e space x equals square root of 3 y space s u c h space t h a t space A B C thin space i s space a space t r i a n g l e
S o space c o o r d i n a t e s space o f space B space w i l l space b e space o f space t h e space f o r m space left parenthesis square root of 3 y comma space y right parenthesis
N o w comma space A B C space i s space a n space e q u i l a t e r a l space t r i a n g l e space w i t h space s i d e space a
rightwards double arrow A B equals a equals B C equals A C
rightwards double arrow A B equals square root of open parentheses square root of 3 y close parentheses squared plus y squared end root equals 2 y equals a
therefore B space i s space open parentheses fraction numerator square root of 3 a over denominator 2 end fraction comma a over 2 close parentheses
N o w comma space C A equals a equals B C
rightwards double arrow c squared plus d squared equals a squared equals open parentheses c minus fraction numerator square root of 3 a over denominator 2 end fraction close parentheses squared plus open parentheses d minus a over 2 close parentheses squared
rightwards double arrow c squared plus d squared equals a squared equals c squared plus fraction numerator 3 a squared over denominator 4 end fraction minus square root of 3 a c plus d squared plus a squared over 4 minus a d
rightwards double arrow square root of 3 c plus d equals a
W h e n space c equals 0 comma space d equals a
H e n c e comma space c o o r d i n a t e s space o f space C space i s space left parenthesis 0 comma space a right parenthesis
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