In an isosceles triangle ABC, the medians intersect at point O.

In an isosceles triangle ABC, the medians intersect at point O. Find the distance from point O to apex B of this triangle if AB = BC = 13cm, BC = 10cm

∆АВС – isosceles. AB = BC. AO, BH, CO – medians.

In an isosceles triangle, the median drawn to the base is the height.

Hence ∆ABH is rectangular and AH = ½ * AC = 5. By the Pythagorean theorem we obtain AB ^ 2 = AH ^ 2 + BH ^ 2.

We find the unknown BH = √ (AB ^ 2 – AH ^ 2) = √ (13 ^ 2 – 5 ^ 2) = √ (169-25) = √144 = 12.

In any triangle, the medians intersect at one point and are divided by the intersection point in a 2: 1 ratio.

Hence it follows that BО: ОН = 2: 1, i.e. there are 3 parts to VN and VN = 12.

Let’s find the value of one part.

12: 3 = 4.

Thus, VO = 2 * 4 = 8.

Answer: VO = 8.