# Find The Angle

Geometry Level 2

In right angled $$\triangle ABC,$$ $$\angle ABC= 90^{\circ}.$$ $$D,E$$ are the midpoints of segments $$BC, AB$$ respectively, and $$M$$ is the midpoint of $$DE.$$ Let $$O$$ be the circumcenter of $$\triangle AMC.$$ Given that $$O$$ lies on line $$BM,$$ find the sum of all possible values of $$\angle BAC$$ in degrees.

Details and assumptions

• The diagram provided is not accurate.

• If $$\angle BAC$$ has only one possibility, that is your answer. For example, if $$\angle BAC$$ can take only one value: $$60^{\circ},$$ then your answer would be $$60.$$

×