The chords AB, BD, CA and CD are drawn from points B and C of the circle centered at point O.
| June 30, 2021 | education
The chords AB, BD, CA and CD are drawn from points B and C of the circle centered at point O. the ABD angle is 52 degrees. find the degree measure of the angle ACD.
Consider a triangle ABD in which the inscribed angle ABD rests on the arc AD, then the degree measure of the arc AD is equal to two degree measures of the inscribed angle ABD.
Arc AD = 2 * 52 = 104.
The angle ACD inscribed in the circle also rests on the arc AD, then its degree measure is equal to half the degree measure of the arc on which it rests.
Angle АСD = 104/2 = 52.
Answer: The angle ACD is 52.
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