Geometric Naming

Hi, I recently took a test in my geometry class in school. One of the
questions was this:

Given isosceles triangle ABC, such that AB=AC. Draw point D on segment
AC such that, BD=AD=BC. Find the measure of angle A.

After seeing the solution given, angle A=36. However, my arguement is
that I could place point D on segment AC such that D and C are
coinciding. The given restrictions would be met, and I would get the
answer of 60 for angle A.

Is there any rule that says a point cannot be named with two different
variables? Or any other fact that would prove my reasoning wrong?

.

Relevant Pages

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