Find the angle between the chord AB, which contracts the arc of 54 degrees, and the diameter of the BC.
| July 3, 2021 | education
Let’s construct the radius OA.
The central angle AOB rests on the arc AB, the degree measure of which, by condition, is 54, then the angle AOB is equal to the degree measure of this arc.
Angle AOB = 54.
The AOB triangle is isosceles, since ОА = ОВ = R, then the angle ОВА = ОАВ.
Angle OAB = OBA = (180 – AOB) / 2 = (180 – 54) / 2 = 63.
Answer: The angle between the diameter and the chord is 63.
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