Find The Angle

Geometry Level 3

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 \(60.\)


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