Segments MA and MB – chords of a circle with a radius of 6 cm. Angle AMB = 30 degrees. Find the chord AB.

By the condition of the problem, the chords MA, MB and AB form a triangle inscribed in a circle with a radius of 6 cm. By the theorem of sines, the ratio of any side of a triangle to the sine of the opposite angle is equal to the diameter of the circumscribed circle. Therefore, AB / sin AMB = 2 * R. Hence AB = 2 * R * sin AMB = 2 * 6 * sin30 = 12 * 0.5 = 6 cm.

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