What is Apollonius Theorem?

Apollonius theorem is a theorem that relates the sides of triangle with its median. According to Apollonius theorem the addition of squares of two sides of triangle is equivalent to the square of half of third side plus square of the median that bisects the third side. By using this theorem, we can easily find the length of sides or median of the triangle.

Apollonius Theorem Statement

Apollonius theorem states that:

The sum of squares of two sides of the triangle is equal to the twice sum of squares of median bisecting third side and the half of the third side.

Apollonius Theorem Formula

The Apollonius theorem formula is given by:

AB² + AC² = 2[AD² + (BC/2)²]

where,

• AB, AC and BC are sides of triangle ABC
• AD is the median bisecting side BC

Apollonius theorem is a theorem relating the length of median and the length of sides of a triangle. It states that the sum of the squares of any two sides of triangle equals to twice the square of half the third side and twice the square on the median bisecting the third side. In this article we will explore the Apollonius theorem, Apollonius theorem statement and Apollonius theorem formula. We will also discuss the Apollonius theorem proof and solve some examples related to it. Let’s start our learning on the topic “Apollonius Theorem.”