# In a circle centered at point O, diameters AD and BC are drawn; the angle OCD is 80 °. Find the OAB angle

May 31, 2020 | Education

| Consider the triangle COD. This triangle is isosceles, because OC and OD are the radii, therefore they are equal.

By the property of an isosceles triangle ∠ODC = ∠OCD = 80 °.

Consider the triangles AOW and COD. ∠DOC = ∠AOB, because they are vertical. СО = DO = OB = OA, because these are the radii of a circle.

Consequently, the triangles AOW and COD are equal (by the first sign). Therefore, ∠OBA = ∠OAB = ∠ODC = ∠OCD = 80 °

Answer: ∠OAB = 80 °.

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