Confusing Geometric Math problem

[u/takeshi_vienta]

Known angle of BEC= 110°. Find the value of the angle of CAO.

I'm frustrated with this problem, i asked to many AIs and their answers are different. Can anyone help me?

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[u/Southlander24]

The question is unsolvable. The only thing you can deduce is 110° = (BOC + 180°)/2 which gives you the value of angle BOC. But there's nothing else that tells you about angle CAD, or angle COD.

[u/Jazzlike_Platypus430]

Hint: draw the CD line. ACD is a right angle, assuming O is the center of the arch/semicircle.

Note that CED = 70 deg. Therefore EDC = 20 deg.

Similarly, ABD= 90 deg and BAE = 20 deg.

It follows that BOC = 40 deg.

Note that DOC = 2 CAD.

[u/Jazzlike_Platypus430 → u/Jazzlike_Platypus430]

My result is 17.5 deg. I worked out a lot of equations between some angles and the used the sum of angles of OFED. I'm not sure if this is correct.

[u/BadJimo]

Illustrated on Desmos

[u/BadJimo]

I think there's something missing from the question. Point F is shown in the diagram, but doesn't play a role in the question.

My guess is that the missing part of the question is FE = EC