Given equilateral triangle ABC, and point P outside of ABC, prove AP + CP BP.

Question

As described above. I'm really confused about this, and in my process of working, I proved AP + BP > CP and BP + CP > AP, but I'm stuck on this one.

Paul M. · Accepted Answer

The details of the proof depend on exactly where you put P, but if P is outside of BC and opposite A, then

CP + BC > BP because the sum of 2 sides of a triangle is greater than the 3rd side

AP>the side of the equilateral triangle by construction, i.e.AP>BC

therefore

CP+AP>BP

Given equilateral triangle ABC, and point P outside of ABC, prove AP + CP > BP.