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 $PA=PB+PC$ then find the value of

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

The answer is 2.00.

3 solutions

Ahmad Saad
Dec 21, 2015

Ajay Mehndiratta
Sep 9, 2015

One easy solution can be used if it is provided that the given expression is constant for all such P. The solution is to suppose that P coincides with any one of the three vertices of the triangle, say , P coincides with C. The PA = a, PB = a and PC = 0.

Kenny Lau
Aug 7, 2015

Reflect the centre along BC and obtain the position of P.

I have no idea if this is the only solution.

Do you know the triangle

The answer is 2.00.

3 solutions

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