MathDB

2

Part of 2019 Macedonia Junior BMO TST

Problems(1)

2019 JBMO TST- North Macedonia, problem 2

Source: 2019 JBMO TST- North Macedonia

5/26/2019
Circles ω1\omega_{1} and ω2\omega_{2} intersect at points AA and BB. Let t1t_{1} and t2t_{2} be the tangents to ω1\omega_{1} and ω2\omega_{2}, respectively, at point AA. Let the second intersection of ω1\omega_{1} and t2t_{2} be CC, and let the second intersection of ω2\omega_{2} and t1t_{1} be DD. Points PP and EE lie on the ray ABAB, such that BB lies between AA and PP, PP lies between AA and EE, and AE=2⋅APAE = 2 \cdot AP. The circumcircle to △BCE\bigtriangleup BCE intersects t2t_{2} again at point QQ, whereas the circumcircle to △BDE\bigtriangleup BDE intersects t1t_{1} again at point RR. Prove that points PP, QQ, and RR are collinear.
JMMOMacedoniaJunior2019geometrycircumcircle