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I assume that it would be an equilateral triangle, but I'm finding it very hard proving it.

I started by drawing a triangle of side lengths a, b and P -(a+b) with angles of alpha, beta and gamma.

I then used the A=(ab*sine(gamma))/2 formula for the area. But have been hitting a definite brick wall. I'm guessing calculus is necessary, but I'm struggling to see how.

Can anyone help?

Thanks,

Unredeemed.