AC and BD are the diameters of the circle with the center O, and the angle ACB = 39. Find the angle ACD.
| August 10, 2021 | education
The triangle BОС is isosceles, since ОВ and ОВ are the radii of a circle, then the angle ОВС = ОВС = АСВ = 39.
The inscribed DBC angle rests on the CD arc, then its degree measure is 2 * DBC = 2 * 39 = 78.
The central angle СОD also rests on the arc СD, then the angle СОD = 78.
The COD triangle is isosceles, since OC = ОD = R, then the angle OCD = ОDС = (180 – COD) / 2 = (180 – 78) / 2 = 102/2 = 510. Angle ACD = OCD = 51.
Answer: Angle ACD is 51.
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