AB-diameter of a circle centered at the point O. BC-chord. The angle AOC is known
| April 25, 2021 | education
AB-diameter of a circle centered at the point O. BC-chord. The angle AOC is known to be 130 degrees. Find the angles of the triangle BOC.
Angles AOC and BOC are adjacent angles, the sum of which is 180, then the angle BOC = 180 – AOC = 180 – 130 = 50.
The ВOС triangle is isosceles, since OB = OС = R, then the angle OВС = OСВ = (180 – ВOС) / 2 = (180 – 50) / 2 = 130/2 = 65.
Answer: The angles of the BOC triangle are 50, 65, 65.
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