The central angle AOB rests on the chord AB so that the angle AOB is 60 °. Find the length of the chord AB if the radius of the circle is 8.

Consider the triangle AOW. AO = OB, because these are the radii of a circle. Therefore, the triangle AOW is isosceles. Therefore, ∠OWА = ∠ОАВ = 60 ° (by the property of an isosceles triangle). We note that ∠АOW is also equal to 60 ° (by the theorem on the sum of the angles of a triangle). 180 ° -60 ° -60 ° = 60 °. Therefore, the triangle AOW is equilateral (by the property of an equilateral triangle). Therefore, OB = OA = AB = 8. Answer: AB = 8.

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