MathDB

2

Part of 2015 IFYM, Sozopol

Problems(1)

Problem 2 of Third round

Source: VI International Festival of Young Mathematicians Sozopol, Theme for 10-12 grade

12/24/2019
Let ABCDABCD be an inscribed quadrilateral and PP be an inner point for it so that ∠PAB=∠PBC=∠PCD=∠PDA\angle PAB=\angle PBC=\angle PCD=\angle PDA. The lines ADAD and BCBC intersect in point QQ and lines ABAB and CDCD – in point RR. Prove that ∠(PQ,PR)=∠(AC,BD)\angle (PQ,PR)=\angle (AC,BD).
geometry