MathDB
sides of triangle ABC form an arithmetic progression, incircle, circumcircle

Source: 2020 Cono Sur Shortlist G2 https://artofproblemsolving.com/community/c1088686_cono_sur_shortlist__geometry

November 30, 2021
geometryincirclecircumcircle

Problem Statement

Let ABCABC be a triangle whose inscribed circle is ω\omega. Let r1r_1 be the line parallel to BCBC and tangent to ω\omega, with r1≠BCr_1 \ne BC and let r2r_2 be the line parallel to ABAB and tangent to ω\omega with r2≠ABr_2 \ne AB. Suppose that the intersection point of r1r_1 and r2r_2 lies on the circumscribed circle of triangle ABCABC. Prove that the sidelengths of triangle ABCABC form an arithmetic progression.
Back to ProblemsView on AoPS