# The bisector drawn to the base of an isosceles triangle is 5cm, and the base of the triangle

**The bisector drawn to the base of an isosceles triangle is 5cm, and the base of the triangle is 8cm. Find the medians of this triangle**

1 task:

In an isosceles triangle, the medians are divided by the point of intersection in a ratio of 2: 1, counting from the apex. Also, the bisector drawn from the top of an isosceles triangle to the base is its median and height. This means that the median BD is divided by the point O as: BO = 2 * 5/3 = 10/3, OD = 5/3.

From the right-angled triangle AOD we find AO: AO = sqrt ((AD) ^ 2 + OD ^ 2) = (sqrt4) ^ 2 + (5/3) ^ 2 = 16 + 25/9 = 144/9 + 25/9 = 169/9 = 13/3;

AK = 3 parts, one part is equal to AK: 3, then AK = 3/2 AO = 3 * 13/2 * 3 = 6.5 cm.

The medians of an isosceles triangle drawn from the vertices at its base are equal, thus the median AK = CM = 6.5 cm.

Answer: 6.5 cm; 6.5 cm vs 5 cm.