In an isosceles triangle ABC, O, the median intersection point, find the distance from point O

In an isosceles triangle ABC, O, the median intersection point, find the distance from point O to apex A if AB = BC = 10 cm.

Since triangle ABC is isosceles, the median BH is also the height of triangle ABC, then triangle ABC is rectangular, from which, according to the Pythagorean theorem, we determine the length of the leg AH.

AH ^ 2 = AB ^ 2 – BH ^ 2 = 100 – 64 = 36.

AH = 6 cm.

By the property of the median, the point of their intersection divides them in a ratio of 2/1 starting from the top, then BO = 4 cm, OH = 2 cm.

From the right-angled triangle AOH, by the Pythagorean theorem, we determine the length of the hypotenuse AO.

AO ^ 2 = AH ^ 2 + OH ^ 2 = 64 + 4 = 68.

AO = 2 * √17 cm.

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