# The center angle of AOB is 60 °. Find the length of the chord AB, on which it rests, if the radius of the circle is 7.

May 31, 2020 | Education

| Consider the triangle AOW. AO = OB, because these are the radii of a circle. Therefore, the triangle AOW is isosceles. Therefore, ∠OWА = ∠ОАВ (by the property of an isosceles triangle).

By the theorem on the sum of the angles of a triangle, we can write:

180 ° = ∠AOB + ∠OBA + ∠BAO

180 ° = 60 ° + ∠OBA + ∠BAO

120 ° = ∠OBA + ∠BAO

And since ∠OBA = ∠BAO, then ∠OBA = ∠BAO = 120 ° / 2 = 60 °.

Therefore, the triangle AOW is equilateral (by the property of an equilateral triangle). Therefore, OB = OA = AB = 7. Answer: AB = 7.

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