In an isosceles triangle abc O-intersection point of the medians Find oa if ab = bc = 10 ac = 16.

In an isosceles triangle, the median drawn to the base also has its height, then triangle ABD is rectangular, and AD = CD = AC / 2 = 16/2 = 8 cm.

Determine the length of the leg BD in a right-angled triangle ABD.

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

ВD = 6 cm.

By the property of the medians, the point of their intersection divides them in the ratio of 2/1, starting the vertices. BO = 2 * OD.

Then OD = BD / 3 = 6/3 = 2 cm.

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

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

AO = 2 * √17 cm.

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