AC is the diameter of the circle, O is its center. ОC = ОВ = ОА. Find the angle OCВ.

univerkov | May 3, 2021 | education

Since AC is the diameter of this circle, the angle AOC is 180 ° (unrolled).

∠AOC = ∠AOB + ∠BOC.

AO = OB = OC ⇒ △ AOB = △ BOC, whence ∠AOB = ∠BOC = ∠AOC / 2 = 180 ° / 2 = 90 °.

The BOC triangle is isosceles, which means ∠OBC = ∠BCO = (180 ° – ∠BOC) / 2 = (180 ° – 90 °) / 2 = 90 ° / 2 = 45 °.

Answer: ∠OCB = 45 °.

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