MathDB
angle relations in a convex ABCD given, double segment wanted

Source: Iranian Geometry Olympiad 2018 IGO Intermediate p2

September 19, 2018
geometryanglesright angle

Problem Statement

In convex quadrilateral ABCDABCD, the diagonals ACAC and BDBD meet at the point PP. We know that ∠DAC=90o\angle DAC = 90^o and 2∠ADB=∠ACB2 \angle ADB = \angle ACB. If we have ∠DBC+2∠ADC=180o \angle DBC + 2 \angle ADC = 180^o prove that 2AP=BP2AP = BP.
Proposed by Iman Maghsoudi
Back to ProblemsView on AoPS