In a circle centered at point O, there are segments AC and BD diameters. Angle AOD = 148. Find the angle ACB.
| March 28, 2021 | education
Angle BOC = AOD = 148 as vertical angles at the intersection of segments AC and OD.
The ВOС triangle is isosceles, since the segments AC and BD are diameters, and then OB = OС = R.
In an isosceles triangle ВOС, the angle OСВ = OBC = (180 – 140) / 2 = 40/2 = 20.
Point O lies on the segment AC, then the angle OCB = CB = 20.
Answer: The ACB angle is 20.
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