Given a regular triangle ABC, O is the center, OM is perpendicular to ABC. Find MA if AB = 6, MO = 2.

Since triangle ABC is regular, O is the center of this triangle, and OM is perpendicular to any of the sides, for example, to the AC side, therefore point M divides the AC side into two equal parts. From this we conclude that AM = AC / 2,

AM = 6/2 = 3.

Answer: AM = 3



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