MathDB
DP // angle bisector of <BEC , ABCD cyclic, DB = DA + DC, AP = BC, BE _|_AD

Source: 2018 Saudi Arabia IMO TST I p3

July 27, 2020
geometryangle bisectorcyclic quadrilateralparallelequal segmentsperpendicular

Problem Statement

Let ABCDABCD be a convex quadrilateral inscibed in circle (O)(O) such that DB=DA+DCDB = DA + DC. The point PP lies on the ray ACAC such that AP=BCAP = BC. The point EE is on (O)(O) such that BE⊥ADBE \perp AD. Prove that DPDP is parallel to the angle bisector of ∠BEC\angle BEC.
Back to ProblemsView on AoPS