Problem 370. Triangle with squares, Circumcircles, Tangent
circles.
Level: Math Education, High School, College, SAT Prep.
The figure shows a triangle ABC with
the squares ABDE, BCFG, and ACHJ. DE extended meet AC and BC
extended at A_{2} and B_{2}, respectively. GF
extended meet AB and AC extended at A_{3} and C_{3},
respectively. JH extended meet BA and BC extended at A_{4}
and C_{4}, respectively. Prove that the circumcircle
of triangle ABC is tangent to circumcircles of triangles A_{2}B_{2}C,
AB_{3}C_{3}, and A_{4}BC_{4}.

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