1985 OIM Problems/Problem 2

Problem

Let $P$ be a point in the interior of equilateral triangle $ABC$ such that: $PA=5,\;PB=7,\; and \; PC=8$ Find the length of one side of the triangle $ABC$

~translated into English by Tomas Diaz. ~orders@tomasdiaz.com

Solution

By Viviani's Theorem, the altitude of the triangle is the sum of the given lengths, or $20$ . It follows that the side length is $\boxed{\frac{40\sqrt3}{3}}$ .

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1985 OIM Problems/Problem 2

Problem

Solution

See also