In a circle with center O, the angle between the radius of the OC and the chord CB
| February 23, 2021 | education
In a circle with center O, the angle between the radius of the OC and the chord CB is twice as large as the angle between the diameter AB and the chord AC. Find these corners.
The ВOС triangle is isosceles, OС = OB, then the angle СВO = ВCO = 2 * X0.
The inscribed angle CAB and the central angle BOС rest on one arc BC, then the angle BOC = 2 * CAB = 2 * X.
Then in the ВOС triangle the angle (2 * X + 2 * X + 2 * X) = 180.
X = 180/6 = 30.
Angle CAB = 300, angle BCO = 2 * 30 = 60.
Answer: The CAB angle is 30, the BCO angle is 60.
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