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Question

If x2+y2+z2=xy+yz+zx, then the triangle is :

A
Isosceles
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B
Right angled
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C
Equilateral
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D
Scalene
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Solution

The correct option is C Equilateral
x2+y2+z2=xy+yz+zxx2+y2+z2xyyzzx=02(x2+y2+z2xyyzzx)=0(x2+y2)+(y2+z2)+(z2+x2)2xy2yz2zx=0(xy)2+(yz)2+(zx)2=0x=y=z
The given triangle is an equilateral triangle

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