In an isosceles triangle ABC O is the intersection point of the medians.

| July 6, 2021 | education

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

Since triangle ABC is isosceles, then its median AD is also its height, then triangle ABD is rectangular, and AD = CD = AC / 2 = 16/2 = 8 cm.

By the Pythagorean theorem in a right-angled triangle ABD, we determine the length of the leg BD.

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

ВD = 6 cm.

By the property of the medians, at the point of their intersection they are divided in the ratio 2 / 1. BO = 2 * OD.

Then ОD = ВD / 3 = 6/3 = 2 cm.

The triangle AOD is rectangular, then, according to the Pythagorean theorem, the length of the segment AO is equal to:

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

AO = 2 * √17 cm.

Answer: From point O to the top of A 2 * √17 cm.



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