The acute angle between the medians drawn from the acute of a right angled isosceles triangle is

Let the coordinates of the right-angled isosceles triangle be O(0, 0), A(a, 0) and B(0, a).

Here, BD and AE are the medians drawn from the acute angles B and A, respectively.

∴ Slope of BD = m₁

Slope of AE = m₂

Let θ be the angle between BD and AE.

tan θ

⇒ cos θ

⇒ cos θ =

⇒ θ

Hence, the acute angle between the medians is