The 60 ° center angle AOB rests on chord AB of length 3. Find the radius of the circle.
| August 11, 2021 | education
The first way.
The AOB triangle is isosceles, since ОА = ОВ = R, and since the AOB angle = 60, the AOB triangle is equilateral.
Then AO = AB = OB = R = 3 cm.
Second way.
We use the formula for the length of a chord of a circle in terms of the radius of the circle.
L = 2 * R * Sin (AOB / 2), where L = the length of the chord AB, R is the radius of the circle, AOB is the central angle that rests on the chord AB.
3 = 2 * R * Sin (60/2).
3 = 2 * R * Sin30.
2 * R = 3 / (1/2) = 6.
R = 6/2 = 3.
Answer: The radius of the circle is 3 cm.
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