MathDB
Perpendicular Circles Like TST Problem

Source: Iran Third Round 2013 - Geometry Exam - Problem 3

September 8, 2013
ratiotrigonometrygeometry unsolvedgeometry

Problem Statement

Suppose line ℓ\ell and four points A,B,C,DA,B,C,D lies on ℓ\ell. Suppose that circles ω1,ω2\omega_1 , \omega_2 passes through A,BA,B and circles ω1′,ω2′\omega'_1 , \omega'_2 passes through C,DC,D. If ω1⊥ω1′\omega_1 \perp \omega'_1 and ω2⊥ω2′\omega_2 \perp \omega'_2 then prove that lines O1O2′,O2O1′,ℓO_1O'_2 , O_2O'_1 , \ell are concurrent where O1,O2,O1′,O2′O_1,O_2,O'_1,O'_2 are center of ω1,ω2,ω1′,ω2′\omega_1 , \omega_2 , \omega'_1 , \omega'_2.
Back to ProblemsView on AoPS