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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