The height of an equilateral triangle is 10 cm. Find the distance of a point equidistant from the sides of this triangle to its side.
A point equidistant from all sides of a triangle is the center of a circle inscribed in this triangle.
Since triangle ABC is equilateral, its height is the median and bisector of the triangle, and the center of the circle, point O, is the point of their intersection.
The medians of the triangle at point O are divided in a ratio of 2/1 starting from the top, then OH = OK = OM = R = BH / 3 = 10/3 = 3 (1/3) cm.
Answer: The distance from the equidistant point to the sides of the triangle is 3 (1/3) cm.
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