MathDB
concyclic wanted, common external tangents of 2 circles meet on circle

Source: 2022 Saudi Arabia IMO TST 4.3

November 1, 2022
geometryconcurrencyConcyclic

Problem Statement

Let A,B,C,DA,B,C,D be points on the line dd in that order and AB=CDAB = CD. Denote (P)(P) as some circle that passes through A,BA, B with its tangent lines at A,BA, B are a,ba,b. Denote (Q)(Q) as some circle that passes through C,DC, D with its tangent lines at C,DC, D are c,dc,d. Suppose that aa cuts c,dc, d at K,LK, L respectively and bb cuts c,dc, d at M,NM, N respectively. Prove that four points K,L,M,NK, L, M,N belong to a same circle (ω)(\omega) and the common external tangent lines of circles (P)(P), (Q)(Q) meet on (ω)(\omega).
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