Well, the reason and logic behind it are in the proofs for it, of which there are several. I like this one:

https://upload.wikimedia.org/wikipedia/commons/thumb/7/7c/Thales%27_Theorem.svg/180px-Thales%27_Theorem.svg.png

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 ∠OBA = ∠OAB.

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 180°, we have:

a + (a + B) + B = 180

2a + 2B = 180

2(a + B) = 180

a + B = 90