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Problem: equilateral triangle A(2,5),B(8,5),C(5,10.196152) [ Calculator, Method and examples ]

Solution:
Your problem `->` equilateral triangle A(2,5),B(8,5),C(5,10.196152)


Here `A(2,5), B(8,5), C(5,10.2)` are the given points

`AB^2 = (8-2)^2 + (5-5)^2 = (6)^2 + (0)^2 = 36 + 0 = 36`

`BC^2 = (5-8)^2 + (10.1962-5)^2 = (-3)^2 + (5.1962)^2 = 9 + 27 = 36`

`AC^2 = (5-2)^2 + (10.1962-5)^2 = (3)^2 + (5.1962)^2 = 9 + 27 = 36`

`:. AB^2=BC^2=AC^2`

`:. AB=BC=AC`

`:.` ABC is an equilateral triangle










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