# Do you know the triangle

**Geometry**Level 4

\(ABC\) is an equilateral triangle where \(AB=a\) and \(P\) is any point in its plane such that \(\color \red{PA=PB+PC}\) then find the value of

\[\large{{\frac{PA^2+PB^2+PC^2}{a^2}}}.\]

\(ABC\) is an equilateral triangle where \(AB=a\) and \(P\) is any point in its plane such that \(\color \red{PA=PB+PC}\) then find the value of

\[\large{{\frac{PA^2+PB^2+PC^2}{a^2}}}.\]

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