# In an isosceles triangle ABC, the point O of the intersection of the Median. Find the distance from point O

In an isosceles triangle ABC, the point O of the intersection of the Median. Find the distance from point O to the vertex A of this triangle if AB = BC = 10 cm AC = 16 cm.

Since BH is the median of the triangle, then AH = CH = AC / 2 = 16/2 = 8 cm.

In an isosceles triangle, the median drawn to the base also has its height, then the AVN triangle is rectangular. By the Pythagorean theorem, BH ^ 2 = AB ^ 2 – AH ^ 2 = 100 – 64 = 36.

BH = 6 cm.

Point O divides the medians in the ratio of 2/1, then OH = BH / 3 = 6/2 = 2 cm.

From the right-angled triangle AON, according to the Pythagorean theorem, AO ^ 2 = AH ^ 2 + OH ^ 2 = 64 + 4 = 68. AO = 2 * √17 cm.

Answer: The length of the segment AO is 2 * √17 cm.

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