Determine the length of the chord subtending the arc at 120 degrees if the radius of the circle is 6 √3.
| July 4, 2021 | education
From the center of the circle, point O, we construct the radii OA and OB.
The AOB triangle is isosceles with sides 6√3 cm and an angle of 120.
By the cosine theorem, we determine the length of the base AB of the triangle.
AB ^ 2 = OA ^ 2 + OB ^ 2 – 2 * OA * OB * Cos120 = 108 + 108 – 2 * 108 * (-1/2) = 324.
AB = 18 cm.
Answer: The chord length is 18 cm.
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