In an isosceles triangle ABC. O-intersection point of the medians. Find the distance from the vertex A

| March 11, 2021 | education

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

The median BD of the isosceles triangle ABC, drawn to the base of the AC, is also its height, then the triangle ABD is rectangular, and AD = CD = AC / 2 = 16/2 = 8 cm.

In a right-angled triangle ABD, according to the Pythagorean theorem, we determine the length of the leg BD.

BD ^ 2 = AB ^ 2 – AD ^ 2 = 100 – 64 = 36.

ВD = 6 cm.

The medians of the triangle, at the point of their intersection, are divided in the ratio of 2 / 1. VO = 2 * OD.

Then ОD = ВD / 3 = 6/3 = 2 cm.

In a right-angled triangle AOD, by the Pythagorean theorem, we determine the length of the segment AO.

AO ^ 2 = AD ^ 2 + OD ^ 2 = 64 + 4 = 68.

AO = 2 * √17 cm.

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



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