The measure of angle ACB is 120 degrees
How to determine the measure of angle ACB?
We have:
Tangent AB = Tangent CB
Since the chord has the same length as the radius of the circle, then the triangle OBA is an equiateral triangle (60 degrees each)
The angle between the point of tangency and the radius is a right angle.
This means that:
60 + x = 90
Solve for x
x = 30
Where x represents the angle BAC
Recall that:
Tangent AB = Tangent CB
So, we have:
Angle BAC = Angle CBA = x = 30
The sum of angles in a triangle is 180.
This gives
Angle BAC + Angle CBA + Angle ACB = 180
Substitute known values
30 + 30 + Angle ACB = 180
Subtract 60 from both sides
Angle ACB = 120
Hence, the measure of angle ACB is 120 degrees
Read more about tangent lines at:
https://brainly.com/question/6617153
