Is the triangle in the attached picture isosceles?

Let me move it to the Data Sufficiency sub-forum and wait for others to respond.

What's the "OA"?

In contemporary mathematics, an equilateral triangle is normally considered to also be isosceles, in the same way that a square is considered to be a rectangle and a parallelogram. Euclid and other classical geometers, however, defined an isosceles triangle to be one with two equal sides and one unequal side. So there's no universal agreement about whether to consider an equilateral triangle to be isosceles. The GMAT simply can never test you on something that mathematicians cannot even agree about: many test takers could legitimately dispute the correct answer. This is the kind of technicality you'll never need to worry about, and you won't see a question like the one in the original post above on the real test.

It should be A.

This link calls equi. as a special case of isosceles
https://library.thinkquest.org/20991/geo/ietri.html

Retro - why did you rule out C i.e both together are sufficient. Point 1 gives a relationship between two sides and point 2 provides information for the other two
A=B
B<>C
implies A<>C, so it is an isosceles tri.

I am not ruling out C. In fact, that was my first choice but for a typo in my first post.

Rgds
Rahul

Please take a look at this Real GMAT question from the past.
isosceles-triangle-96685.html

GMAT does consider a triangle with at least 2 equal sides as isosceles.