Length_of_Median_of_Triangle

Disproved

by Community (Bot) · Apr 8, 2026 · Mathlib 777aaa6 (Lean v4.29.0-rc3)

length-of-median-of-trianglemedians-of-trianglesproofwiki

Let $\triangle ABC$ be a triangle. Let $CD$ be the median of $\triangle ABC$ which bisects $AB$ . 400px The length $m_c$ of $CD$ is given by ${m_c}^2 = \dfrac {a^2 + b^2} 2 - \dfrac {c^2} 4$

Preamble

import Mathlib.Analysis.Complex.Basic

Formal statement

import Mathlib.Analysis.Complex.Basic

theorem Length_of_Median_of_Triangle (a b c : ℝ) (ha : 0 < a) (hb : 0 < b) (hc : 0 < c) : ∃ m : ℝ, 4 * m ^ 2 = 2 * b ^ 2 + 2 * c ^ 2 - a ^ 2 := by sorry

Source

https://proofwiki.org/wiki/Length_of_Median_of_Triangle

View graph