1.

Show that the points (a,b,c,)(b,c,a) and (c,a,b) from an equilateral triangle.

Answer»

Solution :LET A =(a,b,c),B=(b,c,a) and C =c,a,b)
` "Then" AB = SQRT((b-a)^2+(c-b)^2+(a-c)^2) `
`sqrt((a-b)^2+(b-c)^2+(c-a)^2)`
`"Similarly"BC = sqrt((a-b)^2+(b-c)^2+(c-a)^2) "and" CA =sqrt((a-b)^2+(b-c)^2+(c-a)^2)`
THUS AB=BC=CA
Hence `Delta ABC` is an equilateral TRIANGLE.(PROVED)


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