# In an isosceles triangle ABC (BC-base), the medians intersect at point O. Find OB if AB = AC = 13cm, BC = 10cm.

The median AH, which is also the height of the triangle in an isosceles triangle, divides the base of the BC in half.

СН = ВН = ВС / 2 = 10/2 = 5 cm.

In a right-angled triangle ACH, we determine the length of the leg AH.

AH ^ 2 = AC ^ 2 – CH ^ 2 = 169 – 25 = 144.

AH = 12 cm.

The medians of the triangle of the intersection point are divided in the ratio of 2/1, then AO = 2 * OH.

3 * OH = AH = 12 cm.

OH = 12/3 = 4 cm.

From the right-angled triangle BOH, we define the hypotenuse BO.

BO ^ 2 = OH ^ 2 + BH ^ 2 = 16 + 25 = 41.

BO = √41 cm.

Answer: The length of the VO segment is √41 cm.

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