MathDB

2

Part of 2016 China Northern MO

Problems(2)

2016 CNMO Grade 10 P2

Source: 2016 China Northern MO Grade 10, Problem 2

2/24/2020
In isosceles triangle ABCABC, ∠CAB=∠CBA=α\angle CAB=\angle CBA=\alpha, points P,QP,Q are on different sides of line ABAB, and ∠CAP=∠ABQ=β,∠CBP=∠BAQ=γ\angle CAP=\angle ABQ=\beta,\angle CBP=\angle BAQ=\gamma. Prove that P,C,QP,C,Q are colinear.
geometry
2016 CNMO Grade 11 P2

Source: 2016 China Northern MO Grade 11, Problem 2

2/25/2020
Inscribed Triangle ABCABC on circle ⊙O\odot O. Bisector of ∠ABC\angle ABC intersects ⊙O\odot O at DD. Two lines PBPB and PCPC that are tangent to ⊙O\odot O intersect at PP. PDPD intersects ACAC at EE, ⊙O\odot O at FF. MM is the midpoint of BCBC. Prove that M,F,C,EM,F,C,E are concyclic.
geometry