MathDB
concurrency related to parallelogma and a circle

Source: 2020 European Mathematical Cup Seniors P1

December 23, 2020
geometryparallelogramconcurrencyconcurrent

Problem Statement

Let ABCDABCD be a parallelogram such that ∣AB∣>∣BC∣|AB| > |BC|. Let OO be a point on the line CDCD such that ∣OB∣=∣OD∣|OB| = |OD|. Let ω\omega be a circle with center OO and radius ∣OC∣|OC|. If TT is the second intersection of ω\omega and CDCD, prove that AT,BOAT, BO and ω\omega are concurrent.
Proposed by Ivan Novak
Back to ProblemsView on AoPS