In a regular triangle ABC, point O is the center. OM is perpendicular to the plane ABC.

In a regular triangle ABC, point O is the center. OM is perpendicular to the plane ABC. Find the distance from point M to side AB, if AB = 10cm, OM = 5cm

Point O, by condition, is the center of an equilateral triangle ABC, and therefore the point of intersection of the medians, which are divided in a ratio of 2/1 starting from the vertex.

Then OH = CH / 3.

Let’s define CH, the height of an equilateral triangle.

CH = AB * √3 / 2 = 10 * √3 / 2 = 5 * √3 cm.

Then OH = 5 * √3 / 3 cm.

From the right-angled triangle MOH, according to the Pythagorean theorem, MH ^ 2 = OM ^ 2 + OH ^ 2 = 25 + 25/3 = 100/3.

MH = 10 / √3 = 10 * √3 / 3 cm.

Answer: From point M to AB 10 * √3 / 3 cm.