The radii OA, OB and OC are drawn in the circle. Find the length of the chord AB if the angle OAB = angle OBC = 55 degrees and BC = 32 cm.
In triangles AOB BOC, the lengths of the sides OB, OB, OC are equal to both the radii of the circle, then the triangles ABO and BOC are isosceles, which means the angle OA = BOC, the angle BOC = BCO.
Since, by condition, the angle ОВС = ОАВ = 55, then the angle ОАВ = ОВА = ОВС = ОАВ = 55.
Angle AOB = BOC = (180 – 55 – 55) = 70, then the triangle AOB = BOC on two sides and the angle between them, which means AB = BC = 32 cm.
Answer: The length of the chord AB is 32 cm.
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