MathDB
\sum |AB_k|^{2} = \sum_{k=0}^{n} |B_0B_k|^2

Source: Irish MO 2017 paper 2 problem 3

December 12, 2022
geometrySum

Problem Statement

A line segment B0BnB_0B_n is divided into nn equal parts at points B1,B2,...,Bn−1B_1,B_2,...,B_{n-1} and AA is a point such that ∠B0ABn\angle B_0AB_n is a right angle. Prove that : ∑k=0n∣ABk∣2=∑k=0n∣B0Bk∣2\sum_{k=0}^{n} |AB_k|^{2} = \sum_{k=0}^{n} |B_0B_k|^2
Back to ProblemsView on AoPS