Proof
We use the following facts: the sum of the angles in a triangle is equal to two right angles (180°) and the base angles of an isosceles triangle are equal.
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Since OA = OB = OC, OBA and OBC are isosceles triangles, and by the equality of the base angles of an isosceles triangle, OBC = OCB and BAO = ABO.
Let α = BAO and β = OBC. The three internal angles of the ABC triangle are α, α + β and β. Since the sum of the angles of a triangle is equal to two right angles, we have
then
or simply
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