Find The Angle

Geometry Level 3

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

Details and assumptions

  • The diagram provided is not accurate.

  • If BAC\angle BAC has only one possibility, that is your answer. For example, if BAC\angle BAC can take only one value: 60,60^{\circ}, then your answer would be 60.60.

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