proving Thales’ theorem with vectors


Let the radius of the circle be r and AB a diameterMathworldPlanetmathPlanetmath of the circle. We make the dot productMathworldPlanetmath calculation


The result shows that  PAPB, i.e. the circumferential angle APB of the half-circle is a right angleMathworldPlanetmathPlanetmath.

Title proving Thales’ theorem with vectors
Canonical name ProvingThalesTheoremWithVectors
Date of creation 2013-03-22 17:47:45
Last modified on 2013-03-22 17:47:45
Owner pahio (2872)
Last modified by pahio (2872)
Numerical id 5
Author pahio (2872)
Entry type Proof
Classification msc 51F20
Classification msc 51F20
Synonym vector proof of Thales’ theorem
Related topic ThalesTheorem
Related topic SumOfVectors
Related topic DifferenceOfVectors
Related topic ScalarSquare
Related topic ParallelogramPrinciple