In a circle with center O AC and BD are diameters. The central angle AOD is 68 degrees. Find the inscribed angle ACB.
| April 27, 2021 | education
Angle BOS = AOD = 68, since they are vertical.
In the triangle BОС, ОB = ОС = R, then the triangle BОС is isosceles.
In a triangle BОС, the angles at the base of BС are equal, then the angle ОСB = (180 – BОС) / 2 = (180 – 68) / 2 = 56.
The angle ACB is equal to the angle OCB of the triangle BOC, the angle ACB = 56.
Answer: The angle ACB is 56.
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