Viviani's theorem

For any interior point P, the sum of the lengths of the perpendiculars s + t + u equals the height of the equilateral triangle.

Viviani's theorem, named after Vincenzo Viviani, states that the sum of the shortest distances from any interior point to the sides of an equilateral triangle equals the length of the triangle's altitude.[1] It is a theorem commonly employed in various math competitions, secondary school mathematics examinations, and has wide applicability to many problems in the real world.

  1. ^ Abboud, Elias (2010). "On Viviani's Theorem and its Extensions". College Mathematics Journal. 43 (3): 203–211. arXiv:0903.0753. doi:10.4169/074683410X488683. S2CID 118912287.