MathDB

G2

Part of 2018-IMOC

Problems(1)

IMOC 2018 G2 (collinearity given + wanted, 4 tangent circles)

Source: https://artofproblemsolving.com/community/c6h1740825p11314688

3/22/2020
Given △ABC\vartriangle ABC with circumcircle Ω\Omega. Assume ωa,ωb,ωc\omega_a, \omega_b, \omega_c are circles which tangent internally to Ω\Omega at Ta,Tb,TcT_a,T_b, T_c and tangent to BC,CA,ABBC,CA,AB at Pa,Pb,PcP_a, P_b, P_c, respectively. If ATa,BTb,CTcAT_a,BT_b,CT_c are collinear, prove that APa,BPb,CPcAP_a,BP_b,CP_c are collinear.
tangent circlescircumcirclegeometrycollinearcircles