The height of an equilateral triangle is 63 mm. Find the distance from the intersection of the bisectors

The height of an equilateral triangle is 63 mm. Find the distance from the intersection of the bisectors of the triangle to its side.

Since the triangle is equilateral, its heights coincide with the bisectors and medians.

The distances from the point of intersection of the bisectors to the sides will be the same, OK = ОМ = ОН.

The point of intersection of the bisectors is the center of a regular triangle, which divides its height by a ratio of 2/1 starting from the vertex.

BO / OH = 2/1.

Then 2 * OH = BO.

BO + OH = 63 cm.

2 * OH + OH = 63.

OH = 63/3 = 21 cm.

Answer: The distance from the point of intersection of the bisectors of the triangle to its side is 21 cm.