In an isosceles triangle ABC with base AC, the medians AE and BD are drawn, intersecting at the point O.

In an isosceles triangle ABC with base AC, the medians AE and BD are drawn, intersecting at the point O. AC = 18 cm. Find OD.

In an isosceles triangle ABC, the median BD is also the height, AD = DC = 18 cm / 2 = 9 cm. The value OD = (1/3) * BD, by the property of dividing by the point of intersection of the medians in the triangle. To find the median BD, you need one more datum, either side AB, or some of the angles in triangle ABC.

If one more data is known, find the value of BD by the formula, and calculate the value of OD = (1/3) * BD. If triangle ABC were equilateral, then;

BD = √ (AB ^ 2 – AD ^ 2) = √ (18 ^ 2 – 9 ^ 2) = √ (324 – 81) = √243 = 9 * √3.