Measure of angle formed by chords and two circles

Question

The following is a question from a practice GRE Math Subject Test:

In the Euclidean plane, point A is on a circle centered at point O, and O is on a circle centered at A. The circles intersect at points B and C. What is the measure of angle BAC?

Now, I drew a picture where the two circles overlap so that they clearly have the same radius. And a solution I looked at said that because these two circles share the same radius, that means the two triangles formed by OBA and OCA are equilateral triangles, but I don't see why that is. Could someone please explain this to me? I'm sure it's a very fundamental geometry thing I don't know, or am just not seeing there.

Answer 1

• OB=OA=OC=radius of the circle centered at O
• AB=AO=AC=radius of the circle centered at A

You have that AO=OA so all the above line segments have equal lengths.