# Isosceles in Threes

Geometry Level 3

In isosceles triangle $$ABC$$, point $$P$$ lies on $$\overline{BC}$$ so that $$\Delta ABP$$ and $$\Delta ACP$$ are both isosceles as well. How many distinct measures of $$\angle B$$ are possible?

For this problem, we will consider equilateral triangles to be isosceles.

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