# The height of an equilateral triangle is 15, determine at what distance from its sides is the intersection

**The height of an equilateral triangle is 15, determine at what distance from its sides is the intersection point of its bisectors.**

By condition, triangle ABC is equilateral, its height BH is also the bisector and median of the triangle. Let’s draw two medians, AK and CP. Their intersection point O divides the BH height in a ratio of 2/1 starting from the top B.

BО / BО = 2/1.

Let BO = 2 * X cm, then X cm, and 2 * X + X = 15.

3 * X = 15.

X = 15/3 = 5 cm.

BО = 2 * 5 = 10 cm.

OH = 15 – 10 = 5 cm.

In an equilateral triangle, point O is the center of both the inscribed and the circumscribed circle, then OP = OH = OK and are equal to the radius of the inscribed circle.

OP = OH = OK = 5 cm.

Answer: The distance from the point of intersection of the bisectors to the sides is 5 cm.